The mystery dogged our family for decades. How could Donut tell time? And not just the approximate time, but the exact moment before the school bus would arrive. Every. Single. Day.

You see, Donut was my husband's dog growing up, from elementary school through high school.

"She was a stray that came to our house when I was about 4," my husband, Matt, says. She had big, brown floppy ears and giant white and black spots on her flanks. "She was a hound mix," Matt says. "We knew she was a hound because she liked to roam," he adds. "We had to be careful not to let her get out because she would roam the neighborhood."

Donut loved to sleep. While Matt and his brother went to school, Donut spent most of her day inside, lying on the living room rug, sleeping — "and chewing on bones," Matt says. "She would also hide the bones under the sofa cushions."

But every weekday, before the bus dropped off the boys, Donut, without fail, would hop up from the rug, go to the back porch and sit by the window.

"She would wait for my brother and me to walk home so she could greet us at the door," Matt says. "She was always punctual. Never early and never late."

Every winter holiday, Matt's family would tell me this fascinating story. And each year, I would tell myself, "I'm going to figure out how Donut does it and write up a story for NPR." But alas, each year I'd get too busy and not have time.

Not this year. This month, I made time to solve the mystery of Donut's time skills. And the wait has been worth it. Because, folks, guess what Donut likely could do? She could smell time, says psychologist Alexandra Horowitz, who studies dog cognition at Columbia University and Barnard College.

"I'm not at all surprised that Donut would be able to predict the arrival of the school bus," says Horowitz.

Dogs, like people, use many environmental cues to estimate the time during the day, she says. They listen to their body's physiological signs, such as a growing rumble in their tummies, hint of drowsiness or a growing need to ... you know, go outside. Just like humans, they have fluctuating hormones that help create a built-in clock in their bodies and minds.

They also look at the amount of light shining into a room or even the angle of the sun. "Both dogs and humans notice, 'Oh, it's getting a little bit dark in the room,' " Horowitz says.

But Donut, she says, likely has another trick up her furry leg that we humans don't use to tell time (or at least we don't realize we use): "That's olfaction," Horowitz says. "Dogs are living in basically an olfactory world, and I think they are able to track time with smells."

When I first heard this theory, I was a bit incredulous. How do you smell something intangible like time? But then Horowitz explained it to me, and I began to realize that maybe I smell time, too. And maybe dogs understand physics in a way that I don't.

Smelling time for Donut, Horowitz says, likely began with Matt's own unique bouquet of scents. "Humans stink, even the very clean among us," she says. "Dogs can recognize their owners by their smell alone."

Not only do we stink, we also leave our stinky signature everywhere we go. "We're always sloughing skin cells and leaving behind little trails of odor," she says. "For example, you can smell if somebody has been in the elevator before [you] if they were wearing a strong cologne."

So imagine, back in the late 1980s, when Matt and his brother were in elementary school getting ready in the mornings. The two boys filled their home with all sorts of smells — the funk of their baseball uniforms and the stink of their dirty socks and the scent of their shampoo.

As Matt and his brother rushed out the door to catch the bus in the morning, their living room would stink to high heaven with the signature scent of two prepubescent boys.

As Donut sauntered over to the rug for her morning nap, she would literally be swimming in Matt's odor molecules. But over time, the scents in the house changed. "The odors would deteriorate, and the smell gets less strong," Horowitz says.

Given Donut's massive nose and her brain that's incredibly tuned to the concentrations of odors, Horowitz says, there's no question Donut noticed the slow diminishment of Matt's scent over the course of the day.

"Absolutely," Horowitz says. "And we know that dogs are especially attuned to the odors of their person."

In fact, Donut didn't simply notice the shift in smell, Horowitz said. She likely used it to predict the future — to predict when the school bus would arrive.

Every school day Matt and his brother would be away from their home for approximately the same amount of time. And right before the school bus arrived, their smell in the house would drop to about the same level.

Donut probably learned to associate that level of odor with the imminent return of Matt and his brother, Horowitz thinks.

So instead of simply seeing time pass on a clock or feeling it pass in her body, Donut literally smelled time pass. "We have to imagine that things we render as visual experiences, dogs might render in olfaction," Horowitz explains. "So they might experience spaces, recognize things and have memories in smell."

On top of that, she says, odors have "time baked into them" in a way that visual cues don't. "Odors that are lying on the ground or on the sidewalk outside tell us — or dogs — about the past. For example, they say who's been there," Horowitz says. "And if there's a breeze coming up the street, that might bear the odor of someone who's coming around the corner. So it's telling us something about our near future."

Horowitz is quick to point out that this time-sniffing is only a hypothesis. Nobody has ever tested it scientifically (although the BBC tested in a more casual way with one family and their pet; the hypothesis stood up to their very unscientific experiment).

Dogs aren't the only ones that likely track time with odors, says neuroscientist Gregory Berns at Emory University. Many animals use scents to track time. Even humans.

"So, for example, you know, we routinely use smell when we check food. When I open up the milk carton, I give it the sniff test to make sure that it hasn't gone bad before I use it," Berns says. "Every animal probably does that to determine whether something's OK to eat. It's biologically adaptive."

Hmm, somehow that human way of "sniffing time" doesn't seem quite as sophisticated as Donut calculating the arrival of the school bus, with minute precision.

That precision also enables dogs to follow scents through space when tracking down missing people, says cognitive scientist Lucia Lazarowski.

"Tracking and trailing dogs are probably using the intensity of odors, based on how old the odor is, to determine the direction of a track or a trail," she says. "So newer, more recent odors are going to be more intense and stronger than odors that have dissipated and are weaker over time."

So even when dogs are keeping track of physical space, they're also tracking time (or vice versa). And in a way, for dogs, time is inextricably woven into space. Which, if you think about, is reminiscent of the way physicists describe and think about time and space: that is, two inseparable ideas combined in one four-dimensional continuum.

Dogs are way smarter than we give them credit for. Who knew that while Matt was in school studying long division, Donut was showing off his mastery of astrophysics.

This story is part of our periodic science series "Finding Time — a journey through the fourth dimension to learn what makes us tick."