A notable inconsistency, or exaggeration:

> we print our maps using the highest resolution mediums available. ... There's no sense printing at a higher resolution than humans are able to perceive. For print, 300 dpi is the gold standard.

Higher resolution media such as https://www.norsam.com/lanlreport.html are around 20000 dpi. Current semiconductor processes https://www.extremetech.com/computing/296154-how-are-process... have feature sizes around 20 nm, which is about 1.3 million dpi.

This is significantly denser than 300 dpi. It's easy to see the difference between a page printed at 300 dpi and one printed at 600 dpi, so I'd say even 300 dpi doesn't reach "higher resolution than humans are able to perceive".

How long have more detailed mediums (or media) been available? In 01949 George Harrison reported improving the control loop of a ruling engine to a precision of, in the medieval units then in use, 0.2 micro-inches (5 nm): https://www.osapublishing.org/josa/abstract.cfm?uri=josa-41-... so that he could cut grooves for a diffraction grating to that precision, which evidently amounts to a precision of 5 million dpi. This seems to have been about a factor of 70 improvement over what Michelson had achieved before 01900. But serious difficulties attended any attempts to use such diffraction ruling engines to cut irregular patterns such as these maps—as well, of course, as limits in the data bandwidth of the necessary control systems.

More detailed media still have been demonstrated; in 01989 hackers at IBM demonstrated the ability to use an STM to position atoms with atomic precision (≈0.1 nm) https://cen.acs.org/analytical-chemistry/imaging/30-years-mo... and in 02013 other hackers at IBM used this technique to make the famous stop-motion animation, "A boy and his atom" out of a few dozen carbon monoxide molecules on a metal surface: https://www.youtube.com/watch?v=oSCX78-8-q0

0.1 nm precision is about 250 million dpi, almost a million times more detailed than Ramble's maps, or a trillion times if you count by detail per unit area. This is almost as high resolution as you're going to get with matter made out of atoms, although you can improve on it by about an order of magnitude by using, say, lithium hydride. But this resolution has been available for something like 30 years now, though you could reasonably argue that xenon atoms adsorbed to cryogenic copper were not an adequately durable medium.

It's an interesting thought to think about a scale model of Earth printed with this resolution. Ramble carefully omitted any quantitative information about the resolution of their elevation models from this post, though in this thread they say their standard DEM data is ⅓", which is 10 meters; you can download free 30-meter-resolution DEM from USGS https://www.usgs.gov/faqs/where-can-i-get-global-elevation-d... and Airbus offers to sell you 12-meter resolution data https://www.intelligence-airbusds.com/imagery/reference-laye.... Much higher-resolution global data almost surely exists but is not available to the public—interferometric microwave SAR from satellites can get down to centimeter resolution https://earthdata.nasa.gov/learn/backgrounders/what-is-sar but is a strategic advantage for change detection (surveillance) and navigation of things like cruise missiles (when GPS is unavailable).

But suppose you have a 1-cm-resolution DEM of Earth, 5.1 exapixels of data (probably about 5 exabytes, 5.1 million terabytes, about US$100 million of disk), as surely the national spying agency of every spacefaring power does. If you were to print a relief map from it at single-atom resolution—0.1 nm—how big would that map be?

Well, the radius of the Earth is 6371 km (the pole-equator distance was supposed to be 10'000 km, which would have made the radius 6366 km, but Humboldt's expedition lamentably made an 0.08% error in their measurements that we must now live with), and scaling that down by the ratio 1cm:0.1nm, or 100 million to 1, we end up with 63.71 mm radius, or 127.4 mm diameter. The scale model of the Grand Canyon would be 19 microns deep and 290 microns wide. The model earth, accurate to the centimeter, would easily fit in your hand, although hopefully it would be equipped with handles so a stray sand grain on your finger wouldn't dig a kilometer-deep trench across Iowa.

You might very reasonably protest that a map that can only be read with an electron microscope, because nearly all its detail is smaller than the wavelength of light, is less than useful. So if we limit the map's resolution to what you can see with visible light—say, 400 nm—its scale is 4000 times larger. Your scale model of Earth would then be 510 meters across, the size of a small town. But you would still need a very fine optical microscope to see most of its detail.

If you printed out sheets of this map on A3 paper, it would take 6.5 million pages, mostly ocean. Each sheet would cover 10.5 km × 7.4 km.

There's still a lot of room at the bottom!