We have to see if their results withstand critical scrutiny. A sea-level scientist not involved in the work, Andrea Dutton of the University of Florida, said the paper had failed to disclose enough detailed information about the field sites to allow her to judge the overall conclusion. But if the work does hold up, the implications are profound. The only possible explanation for such a large, rapid jump in sea level is the catastrophic collapse of a polar ice sheet, on either Greenland or Antarctica.

Dr. O’Leary is not prepared to say which; figuring that out is the group’s next project. But a 17-foot rise in less than a thousand years, a geologic instant, has to mean that one or both ice sheets contain some instability that can be set off by a warmer climate.

That, of course, augurs poorly for humans. Scientists at Stanford calculated recently that human emissions are causing the climate to change many times faster than at any point since the dinosaurs died out. We are pushing the climate system so hard that, if the ice sheets do have a threshold of some kind, we stand a good chance of exceeding it.

Another recent paper, by Anders Levermann of the Potsdam Institute for Climate Impact Research in Germany and a half-dozen colleagues, implies that even if emissions were to stop tomorrow, we have probably locked in several feet of sea level rise over the long term.

Benjamin Strauss and his colleagues at Climate Central, an independent group of scientists and journalists in Princeton that reports climate research, translated the Levermann results into graphical form, and showed the difference it could make if we launched an aggressive program to control emissions. By 2100, their calculations suggest, continuing on our current path would mean locking in a long-term sea level rise of 23 feet, but aggressive emission cuts could limit that to seven feet.

If you are the mayor of Miami or of a beach town in New Jersey, you may be asking yourself: Exactly how long is all this going to take to play out?

On that crucial point, alas, our science is still nearly blind. Scientists can look at the rocks and see indisputable evidence of jumps in sea level, and they can associate those with relatively modest increases in global temperature. But the nature of the evidence is such that it is hard to tell the difference between something that happened in a thousand years and something that happened in a hundred.