Alan Turing, the father of theoretical computer science, made a proposal that has put AI development on a flawed path for three-quarters of a century, a prominent computer scientist has argued.
In his provocative new analysis in Turing’s Mistake: Escaping the Yoke of Unintelligent Machines, Peter J. Denning tells us that Turing’s stance in 1950 reflected a belief held by the scientific community at the time: that human intelligence can exist without a body – and can therefore emerge in software on digital computers.
Denning also challenges the belief that machine intelligence can be confirmed through an imitation game (now known as the Turing test).
“These two claims have shaped much of AI research and development,” Denning writes. “My premise is that our acquiescence to these claims has led to the AI mess in which we find ourselves today.”
He argues that the artificial intelligence (AI) society is headed for won’t yield a human-level intelligence, known as artificial general intelligence (AGI) – instead it will be dangerous, he warns.
The tacit knowledge problem
At the core of Denning’s argument lies a concept called tacit knowledge. Tacit knowledge represents the vast area of human understanding that cannot be articulated in words or captured in any symbolic form that machines can process.
Denning identifies five major domains of tacit knowledge that he says ‘elude machine learning’. These include common sense knowledge, our daily interactions with others and our environment, our feelings and perceptions, performance skills, and our social and historical culture.
Humans have tried to catalogue common sense knowledge. Beginning in the 1980s, Douglas Lenat’s ambitious Cyc project attempted to compile a comprehensive database of common-sense facts. After 40 years of human effort, it had accumulated 25 million entries.
“Yet even this treasury could not add up to a background of common sense sufficient to make expert systems smart enough to be experts,” Denning notes. “Cyc validated that much of the knowledge that makes people experts cannot be articulated as propositions.”
Performance skill presents another insurmountable barrier.
“Our performance skills in thousands of domains cannot be communicated to machines,” Denning explains. “Whereas descriptions of skillful outcomes (‘know what’) can often be represented as bits and stored in a machine, we do not know how to encode the embodied knowledge for skillful performance (‘know how’).”
Musicians demonstrate this this gap. Denning says: “A virtuoso violinist can play beautiful music yet cannot describe to an acolyte how to produce it.
“Even if a robot could observe and imitate skilled humans, having no biological body, a robot cannot grasp how the musician feels when playing beautiful music or how an audience feels when hearing it.”
Other examples of tacit knowledge include intuitions, gut feelings, spontaneous creativity, and imagination.
The unbreachable barrier
The barrier to all of this is what Denning identifies as ‘the representation problem’.
This fundamental obstacle to achieving human-level AGI is because for any computation to occur, data and instructions must be encoded in physical forms that machines can recognise and process. But tacit knowledge, by its very nature, resists such encoding.
“Behind every word is a deep well of tacit knowledge that gives it meaning,” Denning says. “Words are but symbolic representations of meanings, not the meanings themselves. Commonly used Large Language Models, such as ChatGPT, Claude and Gemini only manipulate words, they cannot know or understand the meaning of what they are saying.”
This creates an unbridgeable divide – because we cannot explain or even understand how tacit knowledge works for humans, we cannot begin to communicate it.
“How we host tacit knowledge is largely a mystery,” Denning admits. “All we know is that it is embodied. We have no idea what we might observe and measure in our bodies to reveal it.”
Context and culture
Beyond individual knowledge, Denning emphasises the role of context – or the circumstances of a situation which gives our statements and actions a broader sense of meaning and purpose.
Context provides innumerable layers of meanings that extend beyond any horizon. Context provides the clue to whether someone is being sarcastic or sincere, or if someone is angry or teasing. Context tells us whether to employ tact or use humour.
“When you inquire into where an assumption of the current context came from, you discover it rests on previous conversations from previous contexts. Each of those in turn rests on further previous conversations and their contexts. This pattern is endless and fractal,” Denning explains.
The cultural dimension of intelligence poses similar challenges.
Culture encompasses our values, norms, judgements, histories, communities and moods, even dynamics of power or care.
“Human conversations are imbued with background assumptions that give meaning and relevance to the words being used,” Denning explains.
“Scaling up LLMs with ever larger neural networks will not enable them to acquire the embodied human knowledge we call culture. LLMs will not attain the objective of the Turing test: to demonstrate machine thought indistinguishable from human thought.”
Ultimately, Denning says there is a mutual incomprehension between humans and machines: artificial neural networks will create a form of machine tacit knowledge that humans cannot understand.
“Machines cannot read our tacit knowledge and we cannot read theirs,” he writes. “We are aliens across an uncrossable divide.”
This has profound implications for AI safety. As machines are unable to read unarticulated human context, aligning them reliably with our intentions may be impossible, Denning warns.
“Through AI automation, agentic networks of machines are likely to develop their own machine intelligence that does not reach the level of human general intelligence but is still quite capable of creating severe problems for humans. This threat is a greater than a take-over by superintelligent machines,” he explains.
“Machine intelligence has different concerns from us and does not appear to care about us. Its ways of thinking and problem-solving look alien to us. We do not yet know how to live safely with these machines.
“Pulling back from an AI automation singularity will demand much from us. We start by accepting that the familiar culture is fading away as intelligent machines appear in our society and we do not know what is coming. We decline to think like machines or be subservient to machines. We refuse to submit to a yoke imposed by low-intelligence machines. Most importantly, we reassert our humanity, declare once again what makes us different from machines, and celebrate those differences.”
When can we trust the results we get from AI, and when is learning impossible? Researchers have shown that there are some problems that even the most powerful AI can reliably solve, no matter how much data it’s given.
The researchers, from the University of Cambridge and the University of California Santa Barbara, designed ‘adversarial’ mathematical systems designed to fool any AI algorithm. Like ethical hackers stress-testing the security of a network, these adversarial systems were designed to map out exactly where and why AI prediction breaks down.
Many real-world systems – like those in oceans, the human brain, or robotics – are too complex to describe neatly with equations, so researchers often learn how they behave by using machine learning. But these AI methods don’t always work well, returning unreliable results or poor predictions.
Sometimes, however, providing reliable solutions is fundamentally impossible, even with infinite data. The adversarial systems developed by the researchers may help developers and users of AI systems know whether they’re working on a solvable or unsolvable problem, build methods that work, and avoid wasting time, effort or AI tokens when a problem is beyond the bounds of possibility.
Their results, reported in the journal Nature Communications, could also help explain why popular AI chatbots like ChatGPT or Claude can be accurate in the short term, but can drift or hallucinate over time.
“We’re probing the boundaries of what you can and can’t do with AI,” said lead author Dr Matthew Colbrook, from Cambridge’s Department of Applied Mathematics and Theoretical Physics. “It’s so important to understand what problems can’t be solved with these methods, because otherwise you end up wasting a lot of time and money.”
Colbrook and his co-authors used an approach called Koopman operator learning, which turns complicated nonlinear behaviour into a linear form that’s easier to analyse.
“What we were doing with these ‘adversaries’ was trying to figure out the types of systems that are hard or impossible to predict, and the types of systems that could be adapted to return reliable results,” said Colbrook.
The researchers identified two main reasons why machine learning breaks down when analysing complex systems: either the algorithm can’t tell when it’s seen enough data to return a reliable result, or patterns in the system can be hidden or hard to distinguish.
“In a lot of AI research, a common assumption is that if we just collect more data, learning will eventually work,” said Colbrook. “But we found this is often wrong. Learning is often layered, and requires multiple steps in the right order to work.”
When a system is chaotic — meaning tiny differences in starting conditions lead to wildly different trajectories, like a choose your own adventure story — the Koopman operator often ends up with a continuous spread of frequencies rather than clean, distinct modes. Short-term prediction was accurate, but long-term prediction became fundamentally unreliable, because the sensitivity to initial conditions compounds over time.
The same mathematical instability that defeats prediction algorithms may also explain why AI chatbots confidently fabricate facts: small changes in a question can send the chatbot down an entirely different path, one that looks plausible word-by-word but loses its grip on reality over longer outputs.
The researchers developed a way to classify these problems based on how many steps are needed to solve them. Where the data is not sufficiently layered or in the right order, the best an algorithm can do – even with infinite data – is 50/50, essentially classifying the problem as unsolvable.
The team also produced a new, provably reliable and highly efficient algorithm with built-in error bounds: essentially giving AI researchers a way to know when they’re able to trust the answer, at a fraction of the cost of most supercomputers.
The researchers tested their approach on over 40 years of Arctic sea ice data. Using their algorithm they found hidden patterns in how the ice is declining, and were able to outperform current leading AI models at a fraction of the cost, on a standard laptop.
“We’re at the stage now where there have been a lot of flashy examples and success stories in AI, but it’s vital that we also ask how certain the models are, and how we know whether they’re certain,” said Colbrook. “Otherwise, we’re building on very shaky foundations.”
Journal
Nature Communications
Article Title
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
Article Publication Date
14-Jul-2026
DSI to lead initiative awarding $1 million in Anthropic Claude AI credits to accelerate AI-enabled research
University of Toronto
Advanced AI models are increasingly becoming a critical research resource, similar to access to data, computing infrastructure, and specialized software. Access to these models, however, can be a barrier for researchers and trainees without the resources to experiment with and deploy frontier AI models in their work.
A gift from AI company Anthropic will provide $1 million in Claude API credits to support research and education at the Data Sciences Institute at the University of Toronto. These usage credits will grant access to Claude’s Application Programming Interface (API), which enables interaction with Claude models. The initiative will equip researchers with access to cutting-edge AI tools that can support discovery, analysis, software development, and innovation across disciplines.
As a hub for research, training, and industry collaboration, bringing together faculty, students, and partners, DSI advances data-driven discovery through interdisciplinary research, training, and partnerships that translate data science into real-world impact. DSI will launch a competitive process for the Claude API credits, leveraging existing grant experience and infrastructure. DSI’s programs, such as the Data Access Grant Program and Research Software Development Support Program, provide a proven model for competitions, with scientific review panels ensuring funding and in-kind support is awarded to high quality, and impactful projects.
Enabling access to emerging data science and AI capabilities across the research community is an important part of DSI's mission. Since 2021, DSI has awarded $19 million in research and trainee funding to more than 500 researchers from across all three U of T campuses and DSI external funding research institutes. DSI member researchers have leveraged these funds to secure over $126 million in external grants enabling researchers to make significant contributions to their fields.
“At DSI we are very pleased to be taking on this role in stewarding and distributing the credits. Opportunities like these to enable applications of AI tools and methodologies are an important part of how we drive research excellence and impact,” says Professor Gary Bader, Associate Director, Research & Software, Data Sciences Institute. “Building on the university’s strong history of leadership in artificial intelligence, the University of Toronto Data Sciences Institute will launch a competitive process to access Claude API credits, with a scientific review panel ensuring they are awarded to safe, high quality and impactful research.”
“The University of Toronto continued advancing neural network research when most of the field had moved on, helping prove it could work at scale. That long-term commitment to getting AI right is something Anthropic is built on, and we’re glad to be supporting future innovative U of T research with Claude,” says Brian Peters, Head of North America Government Affairs at Anthropic.
The initiative strengthens U of T's position as a global leader in AI and interdisciplinary research. The university ranks among global leaders for the study of data science and artificial intelligence, ranking thirteenth in the 2026 QS World University Rankings.
“U of T has a strong history of leadership in artificial intelligence. This new initiative with the Data Sciences Institute, will provide access to cutting-edge AI tools to researchers and will open new possibilities for discovery, analysis, and innovation across the university,” highlights Leah Cowen, Vice-President, Research and Innovation, and Strategic Initiatives, University of Toronto.
Full details of the call for applications for this new initiative are now available. The competition will run from July 20 to September 25, 2026.
