The sky was clear and the air crisp and fresh as I headed to the Public Theater this week to catch a preview of “Deep History,” a one-man show tracing a particularly disastrous bushfire season in Australia. Down the coast, though, Hurricane Milton was barreling toward communities still struggling to recover from his predecessor, Helene.

That irony was surely not lost on David Finnigan, the creator and star of “History,” which arrives at New York following runs at the Edinburgh Fringe Festival and at Mr. Finnigan’s hometown, Canberra, Australia’s capital city, which was hard hit by those fires roughly five years ago. The playwright is an artist who has for the past two decades collaborated with scientists — among them his father, a climate expert who, will we learn, inadvertently launched this project.

As those fires were surging toward the end of 2019, an old injury that flared up landed the elder Mr. Finnigan in the hospital, where while under the influence of painkillers he tasked his son with organizing notes for a paper he had been working on into a rough draft. The paper would explore human society as a thermodynamic system, focusing on six key turning points that each changed the course of humanity.

“We’re a teenage species,” Mr. Finnigan remembers his stoned father telling him during a phone call from his hospital bed. “If you compare the life of the human species to a human individual — you can see that this crisis we’re going into, the climate era, is just the next challenge to be survived for us to make it through to adulthood.”

Over the rest of its roughly 70 minutes, “History” takes us back to the 72 hours preceding New Year’s Day in 2020, when Mr. Finnigan tried to fulfill his father’s assignment. “I’m about to transform into a younger, fresher version of myself through the power of acting,” the writer and performer, who is in fact spry, fit, and barely into his 40s, quips.

What follows resembles a TED talk as much as a play, as Mr. Finnigan, armed with a laptop computer (his credits mention that he’s a game designer as well) and abetted by Hayley Egan’s video design, uses his father’s template to take us on a journey that stretches back 75,000 years, using a female protagonist who is “reincarnated in different bodies” as she travels through Asia, Africa, America, Europe, and, naturally, Australia.

Initially buoyed by his own optimism, Mr. Finnigan paints a lyrical portrait of a woman who hurtles past a volcanic eruption that destroys most of her species, into the Ice Age and the Neanderthal era and the arrival of European settlers in America and onward. “Maybe she’s always jumping ahead to plan the next party,” Mr. Finnigan suggests while introducing his heroine, to make her more relatable. “Maybe she’s curious and that curiosity gets her in trouble. Maybe she can’t help laughing at the exact wrong moment.”

This is illustrated engagingly in vignettes that are sprinkled with statistics, many of them unsettling. It’s as if Mr. Finnigan is folding a bitter pill into a rich, exotic dessert — except that between anecdotes he keeps returning, with increasing alarm, to 2019, where back in Canberra a close friend with a young family is battling the fires as they grow increasingly catastrophic, making it nearly impossible to breathe even indoors.

In his frustration, our narrator finds it hard to sustain his idealism. He reveals his personal experience with “climate deniers,” and grapples with his own takeaway lessons even as he writes them down for the audience to absorb. “Taking power feels wrong, not taking power feels wrong — I don’t know,” Mr. Finnigan laments at one point. 

It’s a neat rhetorical trick — which is not to say that Mr. Finnigan ever comes across as insincere, or that his cause lacks urgency. In full disclosure, I’m married to an anthropologist who frequently deals with climate change in his work, and while he didn’t learn anything new here, he thought Mr. Finnigan made a strong and accessible argument for an undeniable fact: that those of us who have greater resources will suffer less as the planet endures increasing duress, but that we will all feel the toll, and should shoulder some responsibility.

“There will be a generation born on the other side of the worst of the crisis,” Mr. Finnigan resolves toward the end, brightening again, “for whom the world will grow more stable rather than less.” That’s something all of us, regardless of where we live or our political perspectives, can hope for.