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Computers might be able to do remarkable things, but new research offers mathematical proof that they cannot replicate human consciousness.

In a recently published paper, "Is Consciousness Computable? Quantifying Integrated Information Using Algorithmic Information Theory," Phil Maguire, co-director of the BSc degree in computational thinking at National University of Ireland, Maynooth, and his co-authors demonstrate that, within the model of consciousness proposed by Giulio Tononi, the integrated information in our brains cannot be modeled by computers.

Consciousness is not well understood. But Giulio Tononi, a psychiatrist and neuroscientist at the University of Wisconsin, Madison, has proposed an integrated information theory (IIT) of consciousness. IIT is not universally accepted, nor does it offer a definitive map of the mind. Nonetheless, it is well regarded as a model for consciousness and has proven valuable in understanding how to treat patients in comas or other states of diminished consciousness.

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One of the axioms of IIT is "Each experience is unified; it cannot be reduced to independent components." This means that a person's experience of a flower, for example, is the product of input from multiple physiological systems -- various senses and other memories -- but that product cannot be reverse engineered. Under this definition, consciousness behaves like a hash function.

"In this paper, we prove that a process which binds information together irreversibly is non-computable," Maguire explained in an email. "If the human brain is genuinely binding information then it cannot be emulated by artificial intelligence. We've proved that mathematically."

We're sorry, Hal. We're afraid we can do that.
Maguire concedes that the human mind might not integrate information in an irreversible process, but he says that does not match human intuition. "We argue that what people mean by the use of the concept 'conscious' is that a system cannot be broken down. If you can break it down, it isn't conscious (e.g. a light switch)."

This is not to say that artificial intelligence cannot behave intelligently or pass the Turing Test. Rather, what Maguire and his co-authors have shown is that there's something fundamentally different between consciousness, at least under Tononi's definition, and artificial intelligence.

"If you build an artificial system, you always know how you've constructed it," explained Maguire in a phone interview. "You know that it is decomposable. You know it's made up of elements that are non-integratable. We can never build a computing system and algorithm that integrates something so completely it can't be decomposed."

Asked whether there's a parallel between the unknowability of consciousness and the unknowability of quantum states, Maguire was cautious.

"Quantum mechanical effects occur when we reach the limits of measurement," he said via email. "Our definitions break down. There are properties that cannot be defined simultaneously. Similarly, if we try to model the integration of the brain, our models will break down. There will be computational properties that cannot meaningfully be defined. This possibility would rule out strong AI. And perhaps the irreversible integration of the brain is what causes quantum superpositions to collapse. But that's speculation for now."

Maguire's paper, co-authored by Philippe Moser (NUI Maynooth, Ireland), Rebecca Maguire (National College of Ireland), and Virgil Griffith (Caltech), is scheduled to be presented at the Annual Meeting of the Cognitive Science Society in Quebec, Canada, in July.

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