WHEN I WAS THREE years old, my father was jailed for resisting the apartheid regime in South Africa. Shortly afterward, my mother was also jailed, for six months. During that time, I stayed with my grandmother, who was a Christian Scientist. My parents weren’t religious, so this was a whole new world to me. I enjoyed the singing, and especially the Bible: I loved the idea of a book that held the answer to everything. But I didn’t want a big Bible; I wanted a little Bible that I could carry around in my pocket.

So I campaigned endlessly for my grandmother to buy me the smallest possible Bible. When she finally did, I took it everywhere. I couldn’t read yet, but that didn’t matter to me. What I most wanted, even at that early age, was to capture and hold the truth, with the certainty and love that it brings.

My father was charged with sabotage and was fortunate to be released after only three and a half years. Others who had been tried on lesser charges were given life terms. On my father’s release from prison, he was held under house arrest but escaped and fled north to East Africa. We followed him there and lived in Tanzania for several years before moving to London, England. There we joined a small community of exiles trying to survive in unfamiliar, damp, and gloomy surroundings. Nevertheless, my parents always held firm to their ideas. “One day,” they told my brothers and me, “there will be a great change, and South Africa will be free.”

It was hard for us to believe them. Throughout the 1970s and 1980s, as I was growing up in England, going to high school and then university, the situation back home seemed hopeless. The apartheid regime was popular with the all-white electorate, and it had powerful allies overseas. South Africa even developed and tested nuclear weapons. The tiny handful of organized dissidents were easily captured and imprisoned. Protests by school students in Soweto were ruthlessly crushed, and the police state took an iron grip.

But then, quite suddenly, everything changed.

The apartheid system was founded on a profoundly wrong premise — that black people are inferior to white people — and this brought its demise. Within the country, the aspirations of the black majority could no longer be contained. External protests also gathered impact as more and more countries boycotted South Africa. In 1993, with Nelson Mandela’s negotiated release from prison, the mood turned. The white minority accepted that apartheid was no longer sustainable, and that the future would have to involve universal suffrage and greater opportunities for all. The change in South Africa was wrought by a simple but undeniable idea: justice — the principle of fairness, equity, and human rights that protects us all. Justice is a cause shared across races, cultures, and religions; it is powerful enough to win many people’s lifetime commitment and, for some, commitment of their lives. If you had to point to the driver of change in South Africa, it would be this one simple notion that prevailed over all the privilege, wealth, and weaponry that the apartheid regime amassed.

My parents were right. A good idea can change the world.

TODAY, WE LIVE IN a worried world that seems short of good ideas. We are confronted by challenges that can feel overwhelming: financial instability, overconsumption and pollution, energy and resource shortages, climate change, and growing inequality. All of these problems were created by humans, and they are all solvable. Yet we seem to be locked in a culture of short-term thinking, of the quick fix and the fast buck. Whereas what each of these problems really needs for its solution is consistent, principled, far-sighted actions extending over many years.

We’re reaching the limits of existing technologies and natural resources. We are in danger of losing our sense of optimism. Can we find smarter ways to manage our planet? Can we make the discoveries that will open up a bright future? Who are we, after all? Are we just the product of a process of random mutation and natural selection, now reaching its terminus? Or are we potentially the initiators of a new evolutionary stage, in which life may rise to a whole new level?

In these chapters, I want to talk about our ability to make sense of reality and to conceive of the universe within our minds. This ability has been a continuous source of powerful ideas, describing everything from the tiniest subatomic particle up to the entire visible cosmos. It has spawned every modern technology, from cellphones to satellites. It is by far and away our most precious possession, and yet it is also completely free to share. If history is anything to go by, the Universe Within us will be the key to our future.

It is not accidental that revolutions take place when they do. The greatest advances have occurred as a result of growing contradictions in our picture of reality that could not be resolved by any small change. Instead, it was necessary to step back, to look at the bigger picture and find a different way of describing the world and understanding its potential. Every time this happened, a whole new paradigm emerged, taking us forward to frontiers we had never previously imagined. Physics has changed the world, and human society, again and again.

The human mind holds these ideas in the balance: how we live together, who we are, and how we place ourselves within reality. Our conceptions greatly exceed any immediate need. It is almost as if the evolutionary process has an anticipatory element to it. Why did we evolve the capacity to understand things so remote from our experience, when they are seemingly useless to our survival? And where will these abilities take us in the future?

How did we first imagine the Higgs boson, and build a microscope — the Large Hadron Collider, capable of resolving distances a billionth the size of an atom — to find it? How did we discover the laws governing the cosmos, and how did we build satellites and telescopes that can see ten trillion times farther than the edge of the solar system, to confirm those laws in detail? I believe society can draw great optimism from physics’ phenomenal success. Likewise, physics can and should draw a greater sense of purpose from understanding its own origins, history, and connections to the interests of society.

What is coming is likely to be even more significant than any past transformation. We have already seen how mobile communications and the World Wide Web are opening up global society, providing information and education on a scale vastly larger than ever before. And this is only the beginning of how our new technologies will change us. So far, our scientific progress has been founded on, but also limited by, our own physical nature. We are only able to comprehend the world in a classical picture. This has been an essential stepping stone in our development, but one that we need to move beyond. As our technological capabilities grow, they will drastically extend our abilities, our experience of the world, and, in time, who we are.

The internet is only a harbinger. Quantum technologies may change entirely the way in which we process information. In time, they may do much more, allowing us to gain a heightened awareness of reality and of the ways the physical world works. As the depth of our knowledge grows, our representations of the universe will achieve much higher fidelity. Our new knowledge will enable technologies that will vastly supercede current limits. They may change our very nature and bring us closer to realizing the full potential of our existence.

As we look ahead our goal should be to experience, to understand, and to be a part of the universe’s development. We are not merely its accidental byproducts; we are the leading edge of its evolution. Our ability to explain the world is fundamental to who we are, and to our future. Science and society’s mission should be one and the same.

Engraved on Karl Marx’s tombstone are these famous words: “The philosophers have only interpreted the world, in various ways. The point, however, is to change it.” Riffing on a quote attributed to Gandhi, I would say, “The point, however, is to be the change.”

I HAVE BEEN FORTUNATE to spend some of my life in Africa, the cradle of humanity. One of my most memorable experiences was visiting the Ngorongoro Crater, the Serengeti, and the Olduvai Gorge, which early human ancestors inhabited nearly two million years ago. There is an abundance of wild animals — lions, hyenas, elephants, water buffalo. Even the baboons are dangerous: a large male weighs nearly a hundred pounds and has enormous incisors. Nevertheless, they are all afraid of humans. If you are camping there and a big baboon tries to steal your food, all you have to do is raise your arm with a stone in your hand, and it will scurry away.

As puny as human beings are, our ancestors acquired dominance over the rest of the animal kingdom. With their new modes of behaviour, standing up and throwing stones, using tools, making fires, and building settlements, they outsmarted and out-psyched all the other creatures. I have seen elephants and water buffalo move away at merely the scent of a lone Maasai approaching, strolling unconcernedly through the bush with...