One of the most intriguing speculative arguments in physics and computer science isn't really about physics or computer science at all. It's about the brain — or more precisely, about consciousness — and it's been going on for decades. Its central question: Is the brain fundamentally like a computer?

The side that says no relies on some seriously outlandish thinking.

Usually researchers combine data from many fMRI scans to find the areas of the brain typically active during certain tasks. Wikimedia/John Graner

On the more conservative side, there are researchers like Scott Aaronson, a respected theoretical computer scientist at MIT. His view, which is more widely accepted, is that because the brain exists inside the universe, and because computers can simulate the entire universe given enough power, your entire brain can be simulated in a computer. And because it can be simulated in a computer, its structure and functions, including your consciousness, must be entirely logical and computational.

In other words, all evidence suggests that your mind is a computer. (There is, of course, a great deal more nuance to his ideas than this, but that is the crux of his view.)

But there's a dissenting view, advanced most forcefully by the mathematical physicist Roger Penrose: That your consciousness emerges from mysterious, exotic physics acting inside your neurons.

Penrose (who, at 84, is responsible for a substantial chunk of our understanding of the shape of the universe) has argued since the 1980s that conventional computer science and physics can not explain the human mind. He laid out his argument in a pair of books published in the late '80s and early '90s, and more recently in a debate with Aaronson at a conference in Minnesota. (Unfortunately, no complete transcript of that debate exists, but Aaronson summarizes it thoroughly on his blog.)

In essence, Penrose argues that human consciousness has certain features and abilities that conventional computers can not replicate. The nature of computers is algorithmic and logical, and the human mind (in Penrose's view) transcends algorithms and logic. The most salient evidence he points to is the capacity of large groups of mathematicians to move toward true solutions for computationally unsolvable problems. (Aaronson disputes this evidence.)

To explain: Computers as we conceive of them rely on and are bound by the physical and logical rules of our universe. They conduct tasks and solve problems through the logic of algorithms. There are certain problems, however, that conventional computers and mathematical logic cannot solve (like whether a given program will stop or simply run forever). And there's another set of problems that computers can theoretically solve, but would require eons to actually return answers for in practice (like finding all the prime number roots of extremely large numbers). This isn't due to power limitations, but rather the fundamental properties of logic and physics in our universe.

If, as Penrose suggests, humans demonstrate the ability to circumvent some of these basic limits on computation, the brain must interact with systems that exist outside the logical, algorithmic universe. And the quantum world is the most likely candidate.

Penrose speculates that there might exist quantum mechanical processes that can turn up answers to questions in ways no current model of a computer (classical or quantum) would allow, and that the human brain might be able to engage with them through tiny structures, or "microtubules," inside neurons. Michael Shermer, a Scientific American columnist, called this idea pure conjecture.

Gerry Shaw/Wikimedia Commons

The details and neuroscience here aren't fleshed out. Penrose doesn't claim to know the exact mechanism by which it all works. By necessity, there’s a step missing from his reasoning:

The brain is too powerful to rely on conventional physics. It must rely on exotic, undiscovered physics of the sort we might find on the quantum scale. Microtubules inside neurons may be small enough to experience quantum effects. ??? The brain uses exotic physics to produce consciousness.

Which is to say: Penrose believes human consciousness is so bizarre and outlandish, we simply must lack a complete enough picture of the physics of our universe to explain it.

While Aaronson disagrees with Penrose's viewpoint, he said in their debate that the radical speculation is, at least on some level, sound:

If anyone thinks [a brain is nothing like a computer], the burden is on them to articulate what it is about the brain that could possibly make it relevantly different from a digital computer. It’s their job! ...

... One of the many reasons I admire Roger is that, out of all the AI skeptics on earth, he’s virtually the only one who’s actually tried to meet this burden, as I understand it! He, nearly alone, did what I think all AI skeptics should do, which is: suggest some actual physical property of the brain that, if present, would make it qualitatively different from all existing computers, in the sense of violating the Church-Turing Thesis. Indeed, he’s one of the few AI skeptics who even understands what meeting this burden would entail: that you can’t do it with the physics we already know, that some new ingredient is necessary.

So there it is: Either the brain is basically a computer, or there's a whole new world of neuroscience and physics out there that we have not yet even begun to discover.

You can read Aaronson's full write-up of their debate here.