We almost didn’t have a future. Seventy-five thousand years ago, an apocalyptic volcanic explosion at Lake Toba in present-day Indonesia darkened the skies with ash and toxic smoke. In the ruin that followed, some researchers believe, only a small, ragged band of humans survived. If this is true, then almost everyone on Earth owes his or her own existence to 2,000 or so hardy individuals. It was their progeny who went on to settle the planet and build the civilizations we know today. They gave us a future. But what, over the course of the next 75,000 years, will it be?

The physicist Michio Kaku begins his new book, “The Future of Humanity,” with the near-extinction at Toba because of his explicit concern with human survival into the distant future. While our Twitter-blinkered culture can barely think past the next election cycle, Kaku goes long in this new work. The timescapes he tours are breathtaking to consider, ranging from the next few centuries to millions of years of continuing human evolution. But prediction, as Yogi Berra once said, is difficult, especially about the future. Kaku believes he has guardrails that can keep his predictions in check, though: the progress of science and technology. Their sure advance, Kaku believes, allows for the extrapolation of what is possible now to a road map of what we might ultimately become.

Kaku is a techno-optimist, as he has shown in his previous books on the future of physics and the future of the mind. In his view, there are frontiers of knowledge and capability all around us that we’ve only begun to explore. From space travel to genetic engineering to encounters with advanced alien civilizations, Kaku says that through science and technology few limits exist that can, or should, constrain us. Given enough time, he argues, we might become as the gods.

The first and most important limit for us to vault past is Earth itself. Kaku opens the discussion as to how humans might become a multiplanet species by quoting Konstantin Tsiolkovsky, the self-taught Russian genius who first conceived of rocket-based space travel: “The Earth is our cradle, but we cannot be in our cradle forever.” While the American space program has seemed rudderless for years, an era of New Space, led by Elon Musk, Jeff Bezos and other high-frontier entrepreneurs, has just begun. They are the ones making tangible accomplishments in lowering the cost of reaching space. (There’s a red Tesla Roadster orbiting Earth as you read this.) The vitality of the New Space movement means the next 200 years may well see humanity move from just exploring space to actually settling it.

Kaku maps the path to become a true multiplanet species, beginning with reaching, and then settling, Mars. This includes “terraforming” — the large-scale alteration of Mars’s atmosphere — for the benefit of its new human inhabitants. (It’s worth noting that on one level the climate change we’ve wrought on Earth now represents a kind of unintentional terraforming.) After Mars, Kaku turns to the science of asteroids and comets, since they will likely serve as resources to be mined or outposts of our expansion.

Cosmically speaking, however, the solar system is nothing more than the neighborhood humanity was raised in. Like all good techno-optimists, Kaku believes growing up must mean getting out to the stars. But to make that jump we may need more than new machines. Instead, radically new versions of humanity itself may be the price the stars exact.

Even the closest suns are so distant it could take centuries, at best, to reach them. This barrier leads Kaku to consider the ways humans might alter their own design to achieve approximations of immortality. Genetic engineering could allow us to correct the preprogrammed decay hiding inside every cell. Then there are “trans-humanist” dreams of liberating consciousness from its biological wetware. Kaku believes we are all reducible to patterns of connected neurons in our brains. Once it’s possible to fully digitize these “connectomes,” travel via gleaming spaceships might be unnecessary. By encoding our connectomes into laser light we could beam directly from one star system to the other. Once received, our encoded consciousness would be downloaded in different machine, or perhaps biological, bodies at each new location.

You would be right to think this sounds like science fiction or to be skeptical that some of it is even possible. (I’m good with terraforming but doubt that we are nothing but our neurons.) But the strength of Kaku’s writing is knowing which science fiction ideas are worth following. Kaku grounds his readers in science happening right now, while throwing open the windows to imagine where it might lead in a thousand years. In this effort he is particularly adept at drawing from the lexicon of popular science fiction. From Marvel’s “Iron Man” to Christopher Nolan’s “Interstellar,” he uses ideas from our shared cultural warehouse as launchpads for questions of the deep future.

But is a future of genetically engineered bodies, or of no bodies at all, the kind anyone would want to inherit? Once, as I extolled the virtues of our cosmic future, a nonscientist friend quipped, “I’m not sure I want to be a sexless space orb.” It’s this important question of what we value that Kaku’s optimism fails to fully comprehend.

The future will be shaped not just by what we can do but by what we will want to do. That pivot is what makes the deep future so hard to imagine. At one point Kaku makes the argument that the genetic divergence of people 75,000 years ago to now is so small that even with genetic engineering we won’t be so different as to be inhuman 75,000 years in the future. But this argument misses an essential point about culture and imagination. Seeing the extraordinary cave paintings of Lascaux, for example, it seems clear our hunter-gatherer ancestors lived a dense, rich experience that differs significantly from our own. The remarkable science fiction stories of Cordwainer Smith (a.k.a. Paul Linebarger, a noted East Asia scholar and C.I.A. expert in psychological warfare) are instructive in this regard. The universe of his series “The Rediscovery of Man,” set tens of thousands of years from now, offers a future rich in symbols and dreams, where technology has irrevocably altered the mythic underpinnings of what it means to be human.

It’s also worthwhile to ask whose future we’re talking about. Most of our popular science fiction visions of the future were written by men (and most of them white). From feminist critiques to the alternative lines of Afrofuturism, I’ve spent a lot of time recently wondering what our imagined futures would look like if more kinds of people were encouraged to imagine them.

But these misgivings don’t detract from the book’s pleasures. Kaku does acknowledge many of the issues, ethical and otherwise, the science raises, at least in passing. While those problems are likely to be central to the future, this book is meant to introduce readers unfamiliar with science to the vast horizons it has already opened and where our journeys toward those frontiers might lead.