While the number counter is a neat effect, I don't think it works in this instance. For starters, the researcher who wrote this would only include the phrase "at the time of writing" specifically to avoid the need for a live-update depth tracker. From a more meta perspective, the only reason I'd expect to see a continuous update feed is if you were going to do something with it other than have it count up predictably.
Also, when you load the page, the depth counter starts at 2347 m. Even taking into account the time it would take to accelerate to terminal velocity, it could not have been falling for more than 3 minutes. "01/██/2018" is considerably more than 3 minutes ago. At the time of writing this comment, it should be nearing a billion meters.
Giving the depth tracker a constant (presumably terminal) velocity implies the presence of both gravity and air resistance on the other side of the hole. One of the first things I noticed is that, at this rate, somewhere in the 55-56 hour range, the depth would exceed the Earth's radius. Then I realized that opens up a lot of questions concerning possibly important matters with simple tests that I would expect the Foundation to perform. What can we tell about the shape of the area beyond? Is it bounded on all sides like an infinite fleshy esophagus, or is it an infinite expanse in all directions with a floating hole affixed in space? What is gravity like in there? If you turn him upside-down and push something up through the hole, does it fall upwards or downwards from your perspective? If upwards, does it continue falling in the same relative direction if you reorient the guy afterwards? If downwards, does all the stuff that he ate previously eventually come back out if he stays upside-down for long enough? Is the acceleration due to gravity constant and coincidentally similar to gravity on Earth's surface, does it vary uniformly based on the gravity local to the hole, or does the gravity at any point inside the hole match the gravity at the same relative point outside the hole? Is there air in there? If no, why is there a terminal velocity for falling objects? If yes, does he continuously belch out air if you depressurize the room he's in, and does the air pressure increase (meaning your depth tracker's terminal velocity keeps decreasing until it is eventually crushed) or stay constant as you continue to drop down?
