The first response many of us have to a cancer diagnosis is terror, horror and the conviction that we’re doomed. For those who haven’t been paying serious ongoing attention to climate chaos, reminders that we are facing catastrophe can bring the same kind of response. But if you’ve been through cancer or been close to people who have, you know that the usual next phase is figuring out what the treatment options are and, in most cases, going all out for them. The good news is going to be that you got approved for a promising new treatment, are responding well, you are in remission, feel healthier, have a good prognosis. That there are things worth doing that make a difference.

Climate change is a nightmare, and this summer’s floods, fires and extreme heat, from China to Siberia to British Columbia, are reminders that the problem is rapidly growing worse. Yet the striking thing about the IPCC report released earlier this month is not the bad news, which is not really news at all for those who have followed the science closely. It’s the clarity about possibilities, which I found hopeful.

What was remarkable in the IPCC report was put most succinctly in University of Leeds climate physicist Piers Forster’s pair of tweets on Monday, outlining the good and bad news from the report. The bad news was familiar: we are seeing “more intense and more frequent” weather extremes. We are close to 1.5C of warming and will reach it by mid-century. But the good news is that there is, Forster reported, “much more certainty that if we get to net zero CO₂ its contributions to further warming [are] also likely to stop”. At net zero, “the temperature change should even start to slowly go into reverse.” That is, we can halt and even reverse some of the devastation.

Or as the report itself put it, on p. 120 of the fifth section:

Deliberate removal of carbon dioxide (CO₂) from the atmosphere could reverse … some aspects of climate change. However, this will only happen … if deliberate removals are larger than emissions. Some climate change trends, such as the increase in global surface temperature, would start to reverse within a few years. Other aspects … would take decades (e.g., permafrost thawing) or centuries (e.g., acidification of the deep ocean) to reverse, and some, such as sea level rise, would take centuries to millennia to change direction.

In other words, it’s a long shot. It will take heroic effort, unprecedented cooperation, and visionary commitment. It would mean making profound changes in our societies, economies, our ways of doing things. But it is possible to do. And we know how to do it.

I wrote to Forster, who wrote back to me that the good news for him began with the advances in scientific understanding and their precision. He wrote:

There is also good news from the new science. We find that the risk of seeing abrupt changes or tipping points in our climate such as the Gulf stream stopping, Antarctic ice sheet sudden collapse, or Amazon forest dieback are low and will be very unlikely indeed if we can hold temperature rise close to 1.5C. Through improved climate projections we know exactly the emission path the planet needs to take to hold temperatures to close to 1.5C of warming; we need to at least halve global emissions by 2034 and reach net zero CO₂ emissions by mid-century.

As one of the big banners at the 2014 climate march in New York City said, “We have the solutions.” We have understood the problem clearly for decades. In this millennium, the solutions – the energy sources, notably wind and solar, to move us away from fossil fuel – have come of age. The remaining obstacles have been political, which means that there’s a lot of money in the fossil fuel industry and the status quo way of doing things. So we need a great groundswell of civil society sufficient to counter these corrosive forces. We need people to transmute that dread and horror into determination, or rather we need more, because so many – scientists, organisers, policymakers, funders – already have.

The urgency is in the air. The UN secretary general, Antonio Guterres, declared, “This report must sound a death knell for coal and fossil fuels, before they destroy our planet. There must be no new coal plants built after 2021. Countries should also end all new fossil fuel exploration and production, and shift fossil-fuel subsidies into renewable energy. By 2030, solar and wind capacity should quadruple and renewable energy investments should triple to maintain a net-zero trajectory by mid-century.” It’s a cry of desperation but also a plan.

Even the usually staid International Energy Agency said in May that we must aim for net-zero emissions and doing so “means huge declines in the use of coal, oil and gas. The pathway is narrow but achievable, and it would bring major benefits for human prosperity and well-being, providing an opportunity to limit global warming to 1.5C. There is no need for investment in new fossil fuel supply in our net zero pathway.” We need to demolish and dismantle the fossil fuel industry by 2030.

One of the seldom-stressed aspects of what climate demands of us is that it is essentially a mandate to build a better world, a cleaner, more equitable, more cooperative world – cooperative with nature as well as with each other. The status quo cannot continue: the paths forward are, more or less, heaven or hell. And if we get to the relative heaven of a post-carbon world, we will see what kind of hell the age of fossil fuels always was, from the foul toxicity of oil, gas and coal and the millions they kill annually to the corruption of our politics.

Ending the age of fossil fuel with its carbon dioxide and methane emissions is the big piece, but there are many pieces, addressing agriculture and diet, construction and transportation, and environmental protection. One of the pieces, which a former IPCC lead author, William Moomaw, emphasises, is forests. “Forests pull about one-third of all human-caused carbon dioxide emissions from the atmosphere each year,” he and the environmental scientist Beverly Law wrote in an article earlier this year. “Researchers have calculated that ending deforestation and allowing mature forests to keep growing could enable forests to take up twice as much carbon.”

There’s a long-running joke that the most effective carbon sequestration technology is called a tree. Forster put it this way: “The other thing I find amazing is that nature continues to work hard to save our asses, with forests and growth in ocean life continuing to suck up much of carbon we emit. In fact the report shows that it is this that makes the net-zero targets work.”

We know what to do. We know how to do it. The only question is whether we will do it, though from activists to scientists many already are, wholeheartedly. The fear of a far worse world should spur us on, but the hope of a better one can motivate us too. At the climate summit in Glasgow in less than three months, public pressure must make the world’s governments commit to saving the world and hold them to it in the years to come.

• Rebecca Solnit is a Guardian US columnist. She is the author of Men Explain Things to Me and The Mother of All Questions. Her most recent book is Recollections of My Nonexistence