I recently noticed a USGS benchmark near the intersection of Route 608 and Pearl Road in Hambden Township. Some of the benchmarks were embedded in a boulder, some were mounted to public buildings, like the Chardon Courthouse steps used to have one, and some were mounted in a cast concrete pillar, that presumably went down to bedrock.
Those benchmarks are a relic of the analog era and are no longer used because they're not accurate. For example, the one by Pearl Road is on an angle. Maybe something hit it, or freeze thaw cycles moved it over the decades. There's another one I took a picture of. It's near the Exit of the Hambden Cemetery also along route 608. It's barely legible, and it is also slightly off axis.
Since 2006, the benchmark locations are no longer even marked on the USGS topographic maps. If you want to find one today, you need to go to the historic USGS topo maps website. For example, this 1994 map includes one marked BM 1343 (feet), which was near my childhood home in Munson Township. It was there in the mid 1980s, but as far as I know, it no longer exists.
The benchmarks were a physical expression of state authority and part of an otherwise invisible mathematical and algorithmic system for establishing property lines and the like. As such, the markers include a nastygram message to not mess with them; some even include verbiage about fines and jail time.
The main function of this system is to consistently represent map locations in terms of spherical coordinates, like GPS latitude and longitude coordinates. As a result of this system, anyone who plots a point on a map can go and walk to it in the physical 3D reality world. If you look at aerial photography via google maps or a county auditor web site, or the USGS maps, the same point on the ground maps to the same set of coordinates. This system is actually defined "by statute", which in this particular case is algorithmic and mathematical, but also somewhat arbitrary.
There are more and more of these types of systems cropping up into the real world, that is, a system that's really "algorithmic" or that exists in a computer somewhere, but also has a real world expression. The Flock corporation cameras are a good example of that. This stuff will be creeping into everyone's life over the next few years. Essentially a bunch of shitbird crooks and corporations will claim "ownership" of this or that thing and start new rent seeking scams, or new "enclosure movements" and lay claim to previously un-owned stuff.
Anyway, the thing I really wanted to point out in this post is the vast difference between these systems, even something like a map and associated geodetic models, and the mental model people use. For example, if you go for a walk in the woods on a well known trail, you "know" the trail as a string of essentially 1D places all tied together by your footsteps. When I ride on the big creek park mountain bike trail, even though I've done the thing like dozens of times, I don't generally know where I am with-respect to a map of the area, but I know the order of the features I'll ride over.
There are many more elaborate forms of mental geography like emotional associations, or giving a place a personality that don't show up on a map at all. For example, in our local Geauga County legend of "the melonheads" Wisner Road is scary and spooky, or the Lundgren Barn in Kirtland where a cult killed a family used to be considered spooky and foreboding for many years after that event.
The park "Hell Hollow" is another great example of mental geography. People often associated low spots with a decent into the underworld, and often think of Hell as cold and still say "It's as cold as hell out there", which was a feature of the Germanic mythology of Hel, rather than the "fire and brimstone" Hell of the christians, which I guess never fully caught on with the Germanic peoples.


