I like your thought experiment to illustrate why Roman numerals make sense for the time. I think you're right! It is more practical given the tools than Arabic numerals.
To respond to the hiking story; I would opt to use binary if I were in the same situation. I think it's a superior system to use especially out in the woods. It's hard to read for many folk unexposed to binary but it allows you to encode lots of base 10 numbers using a few items. For example, a twig rotated 0 degrees could signify 0, and a twig rotated 90 degrees could be 1. 5 twigs gets you 0 - 31!
To bring it back to the Romans... I realize Binary wasn't commonly used in the Ancient World and that is something I find a little baffling. Base 2 seems like it would be more useful in a pre-pen and paper world, especially when you have to etch something. The closest thing I can find is the Inca Quipu ("talking knots") but even that encodes base 10 numbers into base 4 knots.
If base 2 was widely used by human beings our fingers could have encoded up to 1024 digits.
Gray code takes a lot of work to learn. It's not very likely that people would have discovered it as a way of counting on their fingers (or with other objects) prior to the development of other number systems. If they had, it would have been extremely hard to teach, learn, or verify that someone was using it properly, without other number concepts to use as a reference!
I learned to count in binary on my fingers in high school, and I can confirm that it's more physically challenging than counting the conventional way, and also harder to remember and communicate numbers without translating them into language.
Although you can only represent 10 values instead of 1024 values, remembering one of those values is also correspondingly about 100 times easier.
Plus, it's easy to teach the direct correspondence between fingers and objects even to children or to illiterate or innumerate adults. We can imagine people using fingers this way for a straightforward matching task: "I saw this many dogs!" "I'll give you this many melons!"
And then it leads to separate "uninterpreted" names for each number of fingers that a person can hold up. After that there's a natural route toward place value with units of either one or two hands.
Even the shapes of the Roman numerals may have originated from chunking "hands" as units:
(although the Romans did use further multiplicative combinations of 5s and 10s, they didn't come up with implicit ways to continue the process indefinitely)
To respond to the hiking story; I would opt to use binary if I were in the same situation. I think it's a superior system to use especially out in the woods. It's hard to read for many folk unexposed to binary but it allows you to encode lots of base 10 numbers using a few items. For example, a twig rotated 0 degrees could signify 0, and a twig rotated 90 degrees could be 1. 5 twigs gets you 0 - 31!
To bring it back to the Romans... I realize Binary wasn't commonly used in the Ancient World and that is something I find a little baffling. Base 2 seems like it would be more useful in a pre-pen and paper world, especially when you have to etch something. The closest thing I can find is the Inca Quipu ("talking knots") but even that encodes base 10 numbers into base 4 knots.
If base 2 was widely used by human beings our fingers could have encoded up to 1024 digits.
How did base n > base 2 evolve?