Why Does the World Exist: An Existentia - By Jim Holt Page 0,82
cat are impinging on the retinas of my eyes. But Platonic Forms aren’t like the cat on the mat. They don’t live in the world of space and time. There are no photons traveling back and forth between them and us. So we can’t perceive them. And if we can’t perceive mathematical objects, how can we possibly come to have knowledge of them?
Plato believed that such knowledge was derived from a previous existence, before we were born, during which our souls communed directly with the Forms; what we know of mathematics—and of Beauty and Goodness, for that matter—thus consists of “reminiscences” from this disembodied existence that preceded our earthly lives. Nobody takes that idea seriously any more. Yet what’s the alternative? Penrose himself had written that human consciousness somehow “breaks through” to the Platonic world when we contemplate mathematical objects. But consciousness depends on physical processes in the brain, and it’s hard to see how such processes could be affected by a nonphysical reality.
When I put this objection to Penrose, he furrowed his brow and was silent for a moment. “I know that’s something philosophers worry about,” he said at length. “But I’m not sure I’ve ever really understood the argument. It’s out there, the Platonic world, and we can have access to it. Ultimately, our physical brains are constructed out of material that is itself intimately related to the Platonic world of mathematics.”
So was he saying that we can perceive mathematical reality because our brains are somehow a part of that reality?
“It’s a little more complicated than that,” Sir Roger corrected me. “Each of the three worlds—the physical world, the world of consciousness, and the Platonic world—emerges out of a tiny bit of one of the others. And it’s always the most perfect bit. Consider the human brain. If you look at the entire physical cosmos, our brains are a tiny, tiny part of it. But they’re the most perfectly organized part. Compared to the complexity of a brain, a galaxy is just an inert lump. The brain is the most exquisite bit of physical reality, and it’s just this bit that gives rise to the mental world, the world of conscious thought. Likewise, it’s only a small part of our conscious thought that connects us to the Platonic world, but it’s the purest part—the part that consists in our contemplation of mathematical truth. Finally, just a few bits of the mathematics in the Platonic world are needed to describe the entire physical world—but they’re quite the most powerful and extraordinary bits!”
Spoken like a true mathematical physicist, I thought to myself. But could it be that these “powerful and extraordinary” bits of mathematics—the bits that preoccupy Penrose—are so powerful that they can generate a physical world all by themselves? Does mathematics carry its own ontological clout?
“Something like that, yes,” Sir Roger said. “Maybe philosophers worry too much about lesser issues without realizing that this is perhaps the greatest mystery of all: how the Platonic world ‘controls’ the physical world.”
He paused for a moment to reflect, and then added, “I’m not saying I can resolve this mystery.”
After a bit of small talk about Gödel’s incompleteness theorems, quantum computation, artificial intelligence, and animal consciousness (“I have no idea whether a starfish is conscious,” Penrose said, “but there should be some observable signs”), my visit with Sir Roger came to an end. I left his penthouse world of Platonic ideas and, after a quick elevator descent, reentered the ephemeral world of sensuous appearances below. Retracing my steps through Washington Square, I walked under the “hanging tree,” past the chess hustlers, and into the crowded plaza around the central fountain, encountering the same chaos of exuberant motion, garish colors, pungent smells, and exotic noises. These people! I thought, What do they know of the serene and timeless Platonic realm? Whether they be tourists or buskers, panhandlers or adolescent anarchists, or even NYU professors of cultural studies taking a shortcut through the square on their way to a lecture, their consciousness never touches the ethereal realm of mathematical abstraction that is the true source of reality. Little did they realize that, despite the abundant sunshine, they were chained in the allegorical darkness of Plato’s cave, condemned to live in a world of shadows. They could have no genuine knowledge of reality. That was open only to those who apprehended the eternal Forms, the true philosophers—like Penrose.
But gradually the spell that Sir Roger had cast on me began to wear off. How could the solemn