Embracing a deep time perspective that looks to the future can help to inspire action, says ecosystem ecologist Elena Bennett. “There’s something about thinking a long way off or thinking kind of radically that just jolts people out of their every day,” she says, “whether that’s their everyday skepticism or their everyday arguments or whatever it is that we do on an everyday basis.”

By showcasing geologic eras that telescope across eons, the exhibition offers a humbling perspective of where humans fit into the mind-boggling time scale. By helping visitors to understand the geologic scale of humanity’s recent impact on the planet, museum creators hope to inspire action on climate change. “The No. 1 question we get from visitors is ‘What can I do?’” says Siobhan Starrs, the exhibition’s project manager. “It feels so big. Just like time feels big. The scale of our impact feels unmanageable.”

The new fossil hall at the Smithsonian National Museum of Natural History is not your average dinosaur exhibit. Rather than focusing on “the age of dinosaurs,” the offerings on display in “The David H. Koch Hall of Fossils – Deep Time” span 3.7 billion years.

The Smithsonian National Museum of Natural History’s new fossil hall is more than a collection of dinosaur bones – it’s a time machine.

To travel forward through time, select the rear entrance. To go backward in time, walk through the front doors. Either way, visitors to tomorrow’s opening of “The David H. Koch Hall of Fossils – Deep Time” will traverse 3.7 billion years. During that time span, Earth experienced five mass extinctions due to climate changes. The most recent one, triggered by a meteor collision 66 million years ago, accounts for the towering T. rex skeleton in the main gallery.

By showcasing geologic eras that telescope across eons, the exhibition offers a humbling perspective of where humans fit into the mind-boggling time scale. It also makes explicit connections between past climate change and present-day global warming influenced by Earth’s relatively recent dominant species. Yet the exhibition presents a surprising tone: optimism.

Contrary to fear-based narratives that we’re about to go the way of the stegosaurus, the museum tells its time-traveling visitors they can change their future. It’s a hope-based model of environmental messaging that, according to some, is the most effective way to spark individual action.

“The No. 1 question we get from visitors is ‘What can I do?’” says Siobhan Starrs, the exhibition’s project manager. “It feels so big. Just like time feels big. The scale of our impact feels unmanageable. ... So we want to inspire people. We’re not going to direct what you can do, but we can show you what other people are doing.”

But first, the world’s largest museum of natural history aims to arouse a sense of awe.

The 31,000-square-foot space includes miniature dioramas, interactive screen displays, and fossilized bones that visitors can touch. The exhibition features dinosaurs with claws like the X-Men’s Wolverine, a lifelike recreation of a coral reef during the Permian geologic period, and fossilized cockroaches that serve as a reminder that the hardy insect will outlast even “The Simpsons.”

Carolyn Kaster/AP A detail of the T. rex skeleton is seen at the Smithsonian National Museum of Natural History during a media preview of a new fossil hall in Washington on June 4. The museum will reopen its dinosaur and fossil hall to the public on June 8 after a seven-year, $110 million overhaul.

During a preview tour of the exhibition, Ms. Starrs points to a diplodocus skeleton whose rollercoaster-shaped contour ends with an elongated neck sloping up to the second-floor railing. With a twinkling smile, she says previous exhibitions portrayed the loping creatures as having drooping tails. Now its tail seems to swish in stylish cursive, reflecting what scientists now know about the role of their stiff tendons.

That’s just one example of how the fossil hall, originally founded in 1911, has updated the science of its exhibits as part of a $110 million overhaul. (The renovation includes a $35 million donation by David Koch, who made his fortune in the petroleum refinery business.) During the project’s seven-year development, Ms. Starrs' team also reconceived the exhibition to offer a deep-time chronology of Earth’s development. They say that perspective helps illuminate the geologic scale of humanity’s recent impact on the planet.

“Hope is the tone that we’ve tried to achieve because we know a sober and scientific assessment of what’s going on now leaves you pretty apprehensive about the future because we have already set in motion really big changes,” says paleontologist Scott Wing, a member of the exhibition’s core team. “There’s also no reason from the fossil record to feel that we’ve endangered life on Earth as a whole, or even really ourselves. We seem to be pretty resilient and the technology we have is pretty good at buffering us from bad environments.”

The museum’s urgent-yet-optimistic message is a stark contrast to apocalyptic stories that often dominate news headlines. For example, this week the Breakthrough National Centre for Climate Restoration, an Australian think tank, declared a “high likelihood of human civilization coming to end” following a cycle of accelerated warming beginning as soon as 2050. The Australian report depicts the sort of “social breakdown and outright chaos” that makes “Mad Max” seem like a documentary.

But that worst-case scenario is predicated on an assumption of dire positive feedback effects in the climate system. The Hall of Fossils includes an example of what positive feedback effects look like. Around 250 million years ago, a self-perpetuating, intensifying loop of greenhouse gas emissions led to a mass extinction – over a period of tens of thousands of years.

“That event was probably originally triggered by volcanic carbon,” says Mr. Wing. “At some point there was a reservoir of organic carbon, like methane, in the seafloor that was triggered to be released as a result of the warming that already happened.”

He notes that he doesn’t think we’re close to anything like that scenario at the moment.

“There is a competition to be gloomy about the future which sounds newsworthy and wise, when in fact it’s the optimists who’ve been right,” says Matt Ridley, a British science journalist who takes a lukewarm – and somewhat controversial – view of dire climate predictions. His 2010 book, “The Rational Optimist: How Prosperity Evolves,” emphasizes the potential for human ingenuity to solve and mitigate environmental problems.

“The idea that we won’t find a way to solve problems caused by climate change seems to me implausible,” Mr. Ridley says. “That doesn't mean we should give up and hope it happens naturally. But it does mean we should step forward optimistically, because the alternative is a counsel of despair which demotivates people rather than encourages them.”

The Age of Humans gallery inside the fossil hall is designed to inspire action. Big-screen videos and interactive kiosk displays show visitors how to emulate individuals who have proactively tackled environmental problems. For example, Afroz Shah, a lawyer in Mumbai, India, enlisted hundreds of neighbors to help him clear 4,500 tons of trash from Versova beach. Before the cleanup, the beach looked something like the trash-compactor scene in “Star Wars.” Afterward it was possible to see the sand once again.

Ecosystem ecologist Elena Bennett has cataloged more than 500 examples of similar bright spots in her Seeds of a Good Anthropocene project. She stresses the importance of initiatives that, like the beach cleanup in India, have a scale-up effect. Ms. Bennett, an associate professor in the McGill School of Environment in Montreal, also believes that positive stories (but not utopian ones) galvanize individuals more than scare tactics do. It’s helpful, she says, to embrace a deep time perspective that looks to the future.

“There’s something about thinking a long way off or thinking kind of radically that just jolts people out of their every day, whether that's their everyday skepticism or their everyday arguments or whatever it is that we do on an everyday basis,” says Professor Bennett.

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Next to the Age of Humans gallery there’s a long bench where visitors can sit next to a bronze statue of Charles Darwin. It’s a place to contemplate, perhaps, the museum’s narrative about Earth’s past, present, and future.

“A lot of museums see their role as being over and above just places that are repositories for the material of human history,” says Alistair Brown, policy director for the London-based Museums Association. “Museums are social spaces. They are places that people go to engage with other people, with their families, with their friends, but also with strangers whom you wouldn’t interact with in normal society. That's very important to that idea about inspiring debates and reflection.”