We’re on the ground in Rio covering the 2016 Summer Olympics.

So far in these Olympics, the 19-year-old freestyle swimming sensation Katie Ledecky has won four medals for the U.S., three of them gold, and shattered the 400-meter world record in stunning fashion. She has just one event left in these games, and it’s the one that rocketed her to prominence in 2012: the 800-meter freestyle. She swam a leisurely 8:12.86 in her qualifying heat on Thursday, which is both an Olympic record and faster than any other woman has ever swum this distance. A repeat swim in the final would assure her a gold medal.

Ledecky’s world record in this event — set somewhat unexpectedly at the Arena Pro Swim Series in January in Austin — is 8:06.68. Even before these Olympics began, people have started to wonder whether she might — someday — be able to achieve the unthinkable:

"Is 8 minutes achievable in your lifetime?" "I don't know, I'm getting pretty close" –@katieledecky#Rio2016 — Allison McCann (@atmccann) August 3, 2016

First, a note on how fast eight minutes would be: Since the ban on body-length and non-textile swimsuits in 2009, no woman other than Ledecky has managed to swim under four minutes in the 400-meter freestyle. So eight minutes would literally mean swimming 800 meters faster than anyone else can swim half the distance. But while that sounds crazy, it’s not out of character: Ledecky already swims the 1,500 meters at a faster pace than any other woman swims the 800 meters, and her present 800-meter time would already put her in the 10 fastest women in the 400 meters in the textile era.

So can she do it? Perhaps even now?

It would definitely take an incredible effort, great even among her great efforts. Using her splits from these Olympics and from her previous best times at each distance, I’ve constructed what this hypothetical 7:59.99 swim would look like, and it doesn’t look easy:

Ledecky tends to pace herself about a half-second faster (per 50 meters) in the 400. She swam the middle lengths of her pre-Olympics 400 record in an average of 30.2 seconds, compared with 30.7 in her 800-meter record. If she follows a similar pattern this time, she’ll need to approximately match that 30.2 — which she can do by essentially swimming exactly her 400-meter race, plus an extra 400 meters in the middle at around 30.4 seconds — barely slower than her worst split in that event of 30.3.

This is a tall order, indeed. But there are reasons to think it’s not impossible. Ledecky improved her best time in the 200 meters by 0.68 seconds, and in the 400 meters by 1.91 seconds. Let’s compare those improvements to what she needs for eight minutes:

A per-lap improvement over 800 similar to what she has done in the 200 and 400 would put her within a few seconds of eight minutes.

Does her preliminary time tell us anything? A time of 8:12.86 is a far cry from 8:00, and many of the best world records set in these games have been preceded by near-misses in the earlier rounds. But as a distance event, and as close to guaranteed of advancing as is possible, Ledecky’s time doesn’t tell us much. She was in a comparable situation in the 2015 World Championships in Kazan, Russia, when she put up 8:19.42 in her preliminary heat, a full 8.42 slower than her then-world record of 8:11. And here’s how that turned out:

She went on to break her record by 3.61 seconds (shattering what was then an 8:10 barrier in the process).

A similar 12.08-second improvement on her leisure heat this year would be 5.9 seconds faster than her record, and would put her at 8:00.78. While a jump that large isn’t necessarily implied by the fact that she has done it before, it at least suggests that such an improvement — which would only be slightly larger than what her times and trends already suggest — is credible. And when you’re that close to such a milestone, who knows. A slightly faster reaction time here, a slightly longer sprint at the end there — plus it will be her last race of the games so she should hold nothing back — and the impossible looks a lot more plausible.