The Emperor's New Mind summary

Is math just a numbers game that humans invented to keep busy? Many philosophers – and even some mathematicians – think so. But the author belongs to another school of thought, the Platonist view. Platonists believe that mathematics is firmly rooted in reality. 

One argument in their favor is that most mathematical ideas come about more like discoveries than inventions. 

Long before the advent of modern science, the ancient Greeks came up with some pretty good theories about the geometry of physical objects. But it wasn’t until Galileo started thinking about gravity and energy in the seventeenth century that we really began to understand the principles that govern our world. 

A little later, Isaac Newton worked Galileo’s ideas into three essential laws of motion. The first one says that an object will remain at rest or continue in motion unless it’s acted on by an external force. The second says that an object’s change in motion is proportional to the external force that acts on it. And the third law of motion says that the forces two objects exert on each other are always equal. 

We can safely categorize the tried-and-tested theories of classical physics as superb. 

A superb theory of physics explains a lot, and does so accurately. It also has a certain beauty and simplicity. Take, for example, Newton’s three laws of motion, which elegantly explain how objects behave here on Earth, and predict the motions of distant stars with relative accuracy – an accuracy upon which Einstein’s relativity theories improved. Moreover, both Newton’s and Einstein’s ideas have been verified by our observations over and over again.

For a while, it seemed that the classical theories of physics, such as Newton’s laws of motion, had the power to explain the whole universe. But when physicists began observing the behavior of molecules, atoms, and subatomic particles, they were shocked. These small particles didn’t behave in a “classical” way at all. 

Take, for instance, protons, photons, and electrons, which often change their position and motion in completely counterintuitive ways. Sometimes they even seem to exist in two places at once! This random movement underlies many properties of physical materials, as well as physical processes such as freezing and boiling.

To show again why quantum theory is so confounding, let’s consider the paradox of Schrödinger’s cat. This is a thought experiment proposed by Erwin Schrödinger to Albert Einstein in 1935, which we’ll alter here slightly for our purposes. 

Imagine a box with a cat inside, constructed so that no outside influence can pass through. There’s a device in the box that can be triggered by a single quantum event – let’s say by a photon hitting a photocell. When the device is triggered, it smashes a bottle with cyanide that kills the cat. So how can we know whether the cat is dead?

What does this all have to do with the human mind? Well, it means that it’s very likely that our minds don’t operate in the strict, deterministic way that the classical worldview suggests. Indeed, the author believes that quantum mechanics plays a crucial role in the way we think.

Let’s take a closer look at how our brain works. The human brain is an organ of incredibly complex design. On the most basic level, there’s a large inner region of white matter that sorts and relays signals, and a thin outer surface of gray matter that processes them. The outer surface is called the cerebral cortex, and it’s where higher cognition and complex computation take place. It’s much thicker in humans than in other animals.

We know a great deal about the structure and function of the brain. What we don’t know is how all these different, complicated, parallel processes give rise to our consciousness. This is where quantum physics could come into play. 

There’s at least one spot where quantum effects are directly involved: the retina. Under the right conditions, a single photon hitting our retina is enough to trigger a nerve signal. It takes about seven photons for us to become aware of them.