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I feel like the article misses the most interesting question about Roman numerals and Roman (Greek really) math. How did the numerical system influence the math

by bhntr3 6y ago

I feel like the article misses the most interesting question about Roman numerals and Roman (Greek really) math. How did the numerical system influence the math that they developed and used? 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/ http://worrydream.com/MediaForThinkingTheUnthinkable/)

k__ 6y ago
"Did the clumsiness of doing calculations in Roman numerals keep them from developing more complex systems of numerical calculation?" Probably? I mean, look what the world achieved after it left roman numerals behind.
- goatinaboat 6y ago
  Probably? I mean, look what the world achieved after it left roman numerals behind. 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.
  - AnimalMuppet 6y ago
    Sure. But they did those things by experience and rules of thumb. They didn't do a real stress analysis on those aqueducts, for instance.
    - mdiesel 6y ago
      For those interested in reading further, the ideal (unloaded) shape of an arch isn't a semicircle, but a catenary. 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.
      - ahazred8ta 6y ago
        "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum -- As hangs a flexible cable, so inverted stand the touching pieces of an arch." (although they figured out at some point that this curve was close to being a parabola)
    - goatinaboat 6y ago
      They didn't do a real stress analysis on those aqueducts, for instance. The Romans tested bridges by having the engineers stand under while a legion marched over.
  - ciceryadam 6y ago
    Plus Eratosthenes and Cleomedes got pretty close on calculating the Earth's circumference.
  - mywittyname 6y ago
    It's pretty likely that architects of the time understood place-based arithmetic and used calculators similar to an abacus, even if society as a whole used Roman numerals. The tools a layman use is sometimes different than what a professional does. 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.
- DNied 6y ago
  > look what the world achieved after it left roman numerals behind. Look what the world achieved after we started wearing button shirts.
  - MaxBarraclough 6y ago
    Perhaps it would be expressed better as Look at what mathematics achieved after it left Roman numerals behind.
    - DNied 6y ago
      Nope. Still an unproven correlation.
setr 6y ago
>Did the clumsiness of doing calculations in Roman numerals keep them from developing more complex systems of numerical calculation? 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/page/n11/mode/2up https://archive.org/details/HogbenMathematicsForTheMillion/p... [1] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_an...
pvg 6y ago
but it's always interested me. There's Morris Kline's Mathematical Thought from Ancient to Modern Times which is 3 glorious fat volumes of just this stuff.
tjoc 6y ago
The Greeks had several competing numeral systems (https://en.wikipedia.org/wiki/Greek_numerals https://en.wikipedia.org/wiki/Greek_numerals) including a decimal based system. What I do not get is how come the Romans adopted (if they adopted from the Greeks) the most unwieldy one.
jacobolus 6y ago
> 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. 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-%20Towards%20a%20History%20of%20Greek%20Numeracy.pdf http://worrydream.com/refs/Netz%20-%20Counter%20Culture%20-%... * * * > 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.

by bhntr3 6y ago

k__ 6y ago

"Did the clumsiness of doing calculations in Roman numerals keep them from developing more complex systems of numerical calculation?" Probably? I mean, look what the world achieved after it left roman numerals behind.

goatinaboat 6y ago
Probably? I mean, look what the world achieved after it left roman numerals behind. 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.
- AnimalMuppet 6y ago
  Sure. But they did those things by experience and rules of thumb. They didn't do a real stress analysis on those aqueducts, for instance.
  - mdiesel 6y ago
    For those interested in reading further, the ideal (unloaded) shape of an arch isn't a semicircle, but a catenary. 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.
    - ahazred8ta 6y ago
      "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum -- As hangs a flexible cable, so inverted stand the touching pieces of an arch." (although they figured out at some point that this curve was close to being a parabola)
  - goatinaboat 6y ago
    They didn't do a real stress analysis on those aqueducts, for instance. The Romans tested bridges by having the engineers stand under while a legion marched over.
- ciceryadam 6y ago
  Plus Eratosthenes and Cleomedes got pretty close on calculating the Earth's circumference.
- mywittyname 6y ago
  It's pretty likely that architects of the time understood place-based arithmetic and used calculators similar to an abacus, even if society as a whole used Roman numerals. The tools a layman use is sometimes different than what a professional does. 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.
DNied 6y ago
> look what the world achieved after it left roman numerals behind. Look what the world achieved after we started wearing button shirts.
- MaxBarraclough 6y ago
  Perhaps it would be expressed better as Look at what mathematics achieved after it left Roman numerals behind.
  - DNied 6y ago
    Nope. Still an unproven correlation.

setr 6y ago

>Did the clumsiness of doing calculations in Roman numerals keep them from developing more complex systems of numerical calculation? 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/page/n11/mode/2up https://archive.org/details/HogbenMathematicsForTheMillion/p... [1] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_an...

pvg 6y ago

but it's always interested me. There's Morris Kline's Mathematical Thought from Ancient to Modern Times which is 3 glorious fat volumes of just this stuff.

tjoc 6y ago

The Greeks had several competing numeral systems (https://en.wikipedia.org/wiki/Greek_numerals https://en.wikipedia.org/wiki/Greek_numerals) including a decimal based system. What I do not get is how come the Romans adopted (if they adopted from the Greeks) the most unwieldy one.

jacobolus 6y ago

> 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. 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-%20Towards%20a%20History%20of%20Greek%20Numeracy.pdf http://worrydream.com/refs/Netz%20-%20Counter%20Culture%20-%... * * * > 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.