What We Cannot Know: Explorations at the Edge of Knowledge in Science and Inquiry

Jul 27, 2017 David Rubenstein rated it it was amazing

Shelves: mathematics, science

This is a fascinating book about the theoretical limits of our knowledge, our ability to make predictions, and to understand the universe. Marcus du Sautoy is a professor of mathematics at Oxford University. A central theme of the book, is to show how mathematics works as a powerful tool in helping us understand nature, and the limits to our understanding of how it works.

The book begins with a discussion of throwing a 6-sided die. With perfect knowledge of the position, velocity, and rotation of This is a fascinating book about the theoretical limits of our knowledge, our ability to make predictions, and to understand the universe. Marcus du Sautoy is a professor of mathematics at Oxford University. A central theme of the book, is to show how mathematics works as a powerful tool in helping us understand nature, and the limits to our understanding of how it works.

The book begins with a discussion of throwing a 6-sided die. With perfect knowledge of the position, velocity, and rotation of the die, is the outcome predictable? Actually, the answer depends on the friction of the table onto which the die is thrown. For certain ranges of friction, chaos prevents predictability.c

So the book relates the story of King Oscar II of Norway and Sweden, who celebrated his 60th birthday by offering a gold medal prize to whomever solved a math puzzle; "Is the solar system stable?" Poincare worked on this puzzle, and submitted a paper analyzing the orbits of two planets and a speck of dust. He showed that they followed periodic paths. The editor of the journal showed a gap in the proof, so Poincare tried to stop publication, but it was too late. Poincare had discovered that small perturbations to a stable orbit could make the system fly apart. This led to the discovery of chaos. In 2009, French astronomers modeled the solar system's stability many times, adding slight perturbations. The orbits of Jupiter and Saturn were very stable, but in 1% of the simulations, Mercury's orbit had a resonance with Jupiter, allowing Mercury to collide with Venus, which then collides with the Earth.

It is well known that the Earth's atmosphere is a chaotic system. A small perturbation leads to unpredictable outcomes. This idea feeds the claims of climate-change deniers, that we cannot predict a change in climate. Sautoy brings up the quote,

Not believing in climate change because you can't trust weather reports is a bit like saying you can't tell when the next wave is going to break on Bondi Beach because you don't believe in tides.

Sautoy gives the clearest explanation of wave-particle duality and some of the paradoxes of quantum mechanics, that I have ever read. He discusses elementary particle physics. He brings up the paradox, that electrons behave as if they have no volume, yet they have mass. But then, what is their density? Is it infinite? Is each electron a tiny black hole?

Sautoy brings up a very interesting aspect of Heisenberg's uncertainty principle. Heisenberg's original paper on the subject is often misunderstood. It is not that the act of observation affects a system. Heisenberg was forced to put that example into his paper in order to get it approved by skeptical editors. Even without a direct interaction with a particle, the product of uncertainties in its position and momentum is limited. It's not that we cannot simultaneously precisely measure position and momentum. It is that they do not exist until we measure them.

Many scientists equate God with "things we cannot know." Heisenberg's uncertainty principle also holds for time and energy. When you look at empty space for a short period of time, there is uncertainty in the energy content; space can never be truly empty. Since energy can change into mass, particles can spontaneously appear in a vacuum. So, there is no need for a creator. Some people give the definition of God as the solution to a question, such as "why is there something rather than nothing?" The trouble with most religions, is that God is then given so many properties that god ends up having nothing to do with the definition. It is like working backwards, conjuring up properties without understanding the original definition. One could define God as the existence of things we cannot know. To declare oneself as an atheist is to mean there is nothing we cannot know. But to say that there are things we cannot know, then, is a proof that God exists.

Cosmology is a science where not all questions are, in principle, answerable. This is a "Copernican" aspect of things. The universe is expanding and in the past seven billion years, the expansion rate has been accelerating. Dark energy is hypothesized as the cause. In the distant future, we won't be able to see other galaxies, as space will have disappeared from view, beyond the sphere of our visible universe. But we will still see the stars in our Milky Way galaxy. So, we are lucky to know that other galaxies even exist. Some day in the far future, this knowledge may be lost.

Sautoy describes an interesting set of experiments designed to fool the brain into thinking that your seat of consciousness is located elsewhere--in another person or even in a Barbie doll! Then there is a fascinating discussion of experiments dealing with consciousness. A group of philosophers believes that science can never solve the problem of consciousness. But, we are reminded of the prediction of the philosopher Comte, who foretold that we would never know what is at the heart of a star.

This book is written in a very accessible style. Sautoy gives crystal-clear explanations. I enjoyed every page of this book, as it gave me different ways to think about the universe, and the role of mathematics in unraveling its mysteries.
...more

54 likes · Like · see review