The book Mathematics for the Million[0] suggests a number of limitations were created from the roman numeral system, largely due to the difficulty of division, making infinite series and even large (and extremely small) numbers difficult to work with, intuit and even see outright. As a specific example, it suggests the Achilles and the tortoise paradox[1] is trivially intuited and resolved in the decimal system, whereas no relationship between each division is made clear in the roman numerals
[0] https://archive.org/details/HogbenMathematicsForTheMillion/p...
[1] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_an...
Greek society was awash with arithmetical calculations. It wasn’t written about probably mostly because it was considered so obvious and commonplace. (Though it’s also a bit hard to say quite what was written about, since we’ve lost the vast majority of the books from the time.)
http://worrydream.com/refs/Netz%20-%20Counter%20Culture%20-%...
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> Did the Greeks (and the Romans) not develop algebra or use Arabic numerals because they weren't that into numbers as compared to geometry?
Algebra and arabic numerals really took off with the introduction of cheap paper and printed books.
It’s really hard to transmit the oral culture of skilled use of a counting board via printed book (we might call it tacit knowledge), but you can pretty straight-forwardly print out a pen-and-paper arithmetic algorithm.
There's Morris Kline's Mathematical Thought from Ancient to Modern Times which is 3 glorious fat volumes of just this stuff.
Probably? I mean, look what the world achieved after it left roman numerals behind.
Look what the world achieved after we started wearing button shirts.
Yet the Romans were able to construct aqueducts that are still standing, and a road network spanning thousands of miles, and many other great feats of civil engineering.
We know that other civilization in the region we adept with arithmetic and geometry. And Rome's straight roads and aqueducts are evidence that their citizens understood the practical applications of such mathematics. So it stands to reason someone in the process understood how to perform arithmetic using a place-based notation. Even if they were only generating calculation tables used by field engineers.
I'm sure people devised clever tools that allowed builders to actually build these structures. Much like a roofer today doesn't need to perform any calculations beyond measurements, because they are taught how to use a speed-square to quickly find the correct angles for cutting rafters.
It sounds so simple: so hangs the chain, stands the arch. Took until Hooke in the 17th century before that was written down, though there are earlier (15th century) examples in architecture.
The Romans were still working on the Greek ideology that the circle was the perfect shape. Not to belittle what they did, but the key advances were really in concrete and having an authoritarian empire giving unprecedented resources to public works.
The Romans tested bridges by having the engineers stand under while a legion marched over.
The Greeks were really into geometry using the compass and straight edge so they actually did a lot of math without really needing numbers at all. They viewed calculation as less worthy of mathematicians and my understanding is that we don't have a lot of evidence for how merchants and engineers did basic calculations since most of the great Greek math texts ignored it.
Algorithms and algebra probably existed in some informal way but they weren't really formalized until the Arabs did it with the help of Arabic numerals.
So, while you can do some calculations in roman numerals or using an abacus, the interesting question to me is: Did the Greeks (and the Romans) not develop algebra or use Arabic numerals because they weren't that into numbers as compared to geometry? Or was it the other way around? Did the clumsiness of doing calculations in Roman numerals keep them from developing more complex systems of numerical calculation?
I'm not an expert on the subject at all but it's always interested me. It makes me think of Bret Victor's Media for Thinking the Unthinkable (http://worrydream.com/MediaForThinkingTheUnthinkable/)