Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

How did anyone do math in Roman numerals? (2017)

washingtoncitypaper.com

Post reply on HN
Print view View original

51–60 of 132 posts

Re: How did anyone do math in Roman numerals? (2017)

#51

Post by pvg »

bhntr3 wrote: post #12

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 t…

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.

Re: How did anyone do math in Roman numerals? (2017)

#54

Post by rrrrrrrrrrrryan »

crazygringo wrote: post #37
Sharlin wrote: post #31

Earlier quoted context omitted.

But that's the thing about Roman numerals: you don't need a placeholder number to represent empty columns. And for "what is XVI subtracted from XVI" they could just use a word meaning "nothing", such as nihil or nihilum . The need for the concept of zero as we understand it really only arises together with a place-value system.

Thanks for explaining that clearly. I've always been so baffled by people who claim that some society didn't have a concept for zero, as if "inventing" zero marks some major advance in intelligence. Every culture has a concept of "nothing" which works for zero. The ancient Greeks debated over whether nothing was a number or not, but that's just a semantic splitting of hairs. At some point a symbol for nothing becomes…

This is interesting to me.

I suspect most HN readers probably live in a world of binary logic where things are either "true" or "false", but I come from data-land, where ternary logic is the norm, and where "zero" is a very different concept than "null".

"Zero" is something that can be compared to other numbers, mathematical operations can be performed on it, etc., but "nothing" is just that... nothing.

I'm sure the ancient Greeks used one term to refer to both concepts, and that's exactly what people are pointing out when they refer to other cultures "inventing" the concept of zero. These cultures correctly realized that these are two distinct concepts, and so they created a new, separate term for zero.

Re: How did anyone do math in Roman numerals? (2017)

#55

Post by IIAOPSW »

crazygringo wrote: post #48
dwohnitmok wrote: post #42

Earlier quoted context omitted.

I think that for the majority of people throughout history, numbers were inseparable from numerals, i.e. notation for numbers. This would explain why people are far more comfortable with the notion of real numbers (which despite their name are very very strange in a lot of ways) than imaginary and complex numbers. Even their names betray the difference. However, one has a common notation that everyone has learned whe…

I would clarify that to say numbers were inseparable from words for them. Writing has only existed a short time of our history, so numerals are pretty recent. And the "meaning" of zero as a number like others along a number line, rather than as mere notation for "nothing", I assume only ever became necessary with the invention of negative numbers. With addition, multiplication and division, zero simply does nothing o…

You need zero for place based notation. Eg 210 is "two in the hundreds place, one in the tens place, none in the ones place." Place based notation gets you representation of multiples all the way to infinity. Otherwise you need to represent multiples with unique symbols like in Roman Numerals. Eg X means 10 no matter how many symbols are to the right of it.

Re: How did anyone do math in Roman numerals? (2017)

#56

Post by [deleted] »

rrrrrrrrrrrryan wrote: post #54
crazygringo wrote: post #37

Earlier quoted context omitted.

Thanks for explaining that clearly. I've always been so baffled by people who claim that some society didn't have a concept for zero, as if "inventing" zero marks some major advance in intelligence. Every culture has a concept of "nothing" which works for zero. The ancient Greeks debated over whether nothing was a number or not, but that's just a semantic splitting of hairs. At some point a symbol for nothing becomes…

This is interesting to me. I suspect most HN readers probably live in a world of binary logic where things are either "true" or "false", but I come from data-land, where ternary logic is the norm, and where "zero" is a very different concept than "null". "Zero" is something that can be compared to other numbers, mathematical operations can be performed on it, etc., but "nothing" is just that... nothing. I'm sure the…

[deleted]

Re: How did anyone do math in Roman numerals? (2017)

#57

Post by mywittyname »

goatinaboat wrote: post #22
k__ wrote: post #18

Earlier quoted context omitted.

"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.

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.

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.

Re: How did anyone do math in Roman numerals? (2017)

#58

Post by sn41 »

It is well-known that the place-value system introduced into Europe from India via the Arabs played an invaluable role in modern arithmetic.

But, if you read the "Sand Reckoner" by Archimedes, what he lays out are the rudiments of a place-value system. He essentially describes the modern notation, but not rules for addition, subtraction, multiplication and division using this notation.

Another tidbit: if you see the recent movie about Shannon "The Bit Keeper", he shows the journalist a mechanical device (he designed?) which can do calculations using Roman numerals.

Re: How did anyone do math in Roman numerals? (2017)

#59

Post by jbit »

sn41 wrote: post #58

It is well-known that the place-value system introduced into Europe from India via the Arabs played an invaluable role in modern arithmetic. But, if you read the "Sand Reckoner" by Archimedes, what he lays out are the rudiments of a place-value system. He essentially describes the modern notation, but not rules for addition, subtraction, multiplication and division using this notation. Another tidbit: if you see the…

I'd never heard of this documentary, so I took a look. I assume you meant "The Bit Player"? ( https://www.imdb.com/title/tt5015534/ ). It looks interesting, and it's on Amazon prime video so I'll give it a watch. Thanks!

Re: How did anyone do math in Roman numerals? (2017)

#60

Post by mantap »

crazygringo wrote: post #37
Sharlin wrote: post #31

Earlier quoted context omitted.

But that's the thing about Roman numerals: you don't need a placeholder number to represent empty columns. And for "what is XVI subtracted from XVI" they could just use a word meaning "nothing", such as nihil or nihilum . The need for the concept of zero as we understand it really only arises together with a place-value system.

Thanks for explaining that clearly. I've always been so baffled by people who claim that some society didn't have a concept for zero, as if "inventing" zero marks some major advance in intelligence. Every culture has a concept of "nothing" which works for zero. The ancient Greeks debated over whether nothing was a number or not, but that's just a semantic splitting of hairs. At some point a symbol for nothing becomes…

If you can debate whether or not zero is a number then you haven't invented it.

If zero might not be a number then you can't state that 0 * n = 0 and 0 + n = n and n - n = 0, etc

Post reply on HN