Roman Mathematics

[M. Porcius Cato]

Roman mathematics has always been puzzling: Why would they use such a weird, non-positional system when there was already a much better one (the Hindu-Arabic) in widespread use? Further, given that they didn't employ a positional notation system, how could they multiply?

 

The rationale for their numeric system may have its origins in mercantile security. In the arabic system, a number like 1039 talents can be easily forged to read 9039 talents. Thus, by simply adding a little circle to the 1, it would be possible to defraud someone of 8000 talents. In contrast, to accomplish the same feat in Roman numerals, one would have to change MXXXIX to MxXXXIX, a change which could be more easily detected.

 

Further, Romans didn't always use their numeric symbols to complete computations. More often, they used a Roman abacus, which did have a bi-quinary coded decimal system. What to do if you left your abacus with that little she-wolf whom you were visiting by the Temple of Venus? Well, there was a method, but it was complex.

[M. Porcius Cato]

To play with really outlandish Roman numerals, visit Roman Numeral Conversion, where you will learn that 3,888,888 = mmmdccclxxxvMMMDCCCLXXXVIII.

[eggers]

Roman mathematics has always been puzzling: Why would they use such a weird, non-positional system when there was already a much better one (the Hindu-Arabic) in widespread use? Further, given that they didn't employ a positional notation system, how could they multiply?

 

The rationale for their numeric system may have its origins in mercantile security. In the arabic system, a number like 1039 talents can be easily forged to read 9039 talents. Thus, by simply adding a little circle to the 1, it would be possible to defraud someone of 8000 talents. In contrast, to accomplish the same feat in Roman numerals, one would have to change MXXXIX to MxXXXIX, a change which could be more easily detected.

 

Further, Romans didn't always use their numeric symbols to complete computations. More often, they used a Roman abacus, which did have a bi-quinary coded decimal system. What to do if you left your abacus with that little she-wolf whom you were visiting by the Temple of Venus? Well, there was a method, but it was complex.

Roman numerals are easiler to carve into stone or wood then the indian/arabic numbers. And it's much older. The romans never actually counted, multiplied, subtracted or divided with their numbers, they used the abacus, or a counting board. Their numbers were only used to record the result. The romans were "if it ain't broke don't fix it" type people, and in their opinion, counting boards were just fine. They only really used maths for logistical purposes where complex formulas aren't really required. Afterall (for example) if you have 1000 soldiers walking to britain and they each want 1 pint of beer each a week until they get there, you don't need trigonomitry to figure out how much to give them so they can get there.

As for security, its the other way round. When the arabic numbers made it to europe it was not well accepted at first. However it's quicker to write arabic number, and easier to play with.

This was not missed by greedy business men. Simple reason, if you lend someone money and charge interest, you can work out how much they own you exactly to several decimal places, and make more money. It may not be much from one person, maybe the for example you lend someone $10 for a year and charge alittle interest. Say you get $10.61 back, not much, but using a counting board you would only get $10.50 back. Using a counting board or abacus you have to round to the nearest whole number, meaning they were losing money. Now say you lend 100,000 or 1,000,000 people $10 for a year. The customer doesn't pay much more so they don't complain, but as a business man, your rolling in money now.

[FLavius Valerius Constantinus]

To play with really outlandish Roman numerals, visit Roman Numeral Conversion, where you will learn that 3,888,888 = mmmdccclxxxvMMMDCCCLXXXVIII.

 

*Frets* just wait till you see the numbers written as words(though I doubt the Romans would want to write in words, but how are you gonna pronounce the number if you can't say the words.) its absolutely horrible to memorize them all, even with the fractions, not to mention memorizing both the cardinal and ordinal variety.

Edited January 16, 2006 by FLavius Valerius Constantinus

[M. Porcius Cato]

If you lend someone money and charge interest, you can work out how much they owe you exactly to several decimal places, and make more money. It may not be much from one person, maybe the for example you lend someone $10 for a year and charge alittle interest. Say you get $10.61 back, not much, but using a counting board you would only get $10.50 back. Using a counting board or abacus you have to round to the nearest whole number, meaning they were losing money. Now say you lend 100,000 or 1,000,000 people $10 for a year. The customer doesn't pay much more so they don't complain, but as a business man, your rolling in money now.

 

But I don't see why a Roman couldn't convert $10 to 1000 pennies to do the calculation. As long as the monetary system is decimal, their counting board should work fine. Am I missing something?

[Sextus Roscius]

*Frets* just wait till you see the numbers written as words(though I doubt the Romans would want to write in words, but how are you gonna pronounce the number if you can't say the words.) its absolutely horrible to memorize them all, even with the fractions, not to mention memorizing both the cardinal and ordinal variety.

 

I know what you are talking about, but due to a ton of practicing I've gotten really good at doing Mathmatics in Roman Numerals. Quite simply, I don't think it bothered them, and it obviously didn't hinder their ability to create fantastic engineering structures. I beleive they simply thought "we have made among the greatest achomplishments in the world, such as our armies, our structures, our politics and culture. All using our number system. Look at the countries that use other systems, we conquered them, if not in military terms, we beat them in an architectural and cultural sense. Why use their number system when ours works perfectly fine and doesn't hinder our capabilities"

[eggers]

If you lend someone money and charge interest, you can work out how much they owe you exactly to several decimal places, and make more money. It may not be much from one person, maybe the for example you lend someone $10 for a year and charge alittle interest. Say you get $10.61 back, not much, but using a counting board you would only get $10.50 back. Using a counting board or abacus you have to round to the nearest whole number, meaning they were losing money. Now say you lend 100,000 or 1,000,000 people $10 for a year. The customer doesn't pay much more so they don't complain, but as a business man, your rolling in money now.

 

But I don't see why a Roman couldn't convert $10 to 1000 pennies to do the calculation. As long as the monetary system is decimal, their counting board should work fine. Am I missing something?

my earlier answer was alittle long winded and alittle vague. Basically the decimal system is far more acturate. That all i was trying to get at.

[M. Porcius Cato]

my earlier answer was alittle long winded and alittle vague. Basically the decimal system is far more acturate. That all i was trying to get at.

A decimal system is no more accurate than a base-12 system or a binary system. Think about it.

[eggers]

A decimal system is no more accurate than a base-12 system or a binary system. Think about it.

Yes your correct there but i thought were were talking about why 1234567890 came into use instead of I II III IV V VI VII VIII IX X etc.

Although the binary system was first created sometime in 3rd century in India BC it was never really used and effectively lost until a guy called Gottfried Leibniz in the 17th century re-invented it. (Since the numbers we use today orginate in India, the ancient indians could use binary just fine, though rarely did as far as i can find.) The romans couldn't use the binary system because they didn't have a Zero.

A base-12 system (or imperial system) was used because it is easily divided by 2, 3 and 4, where as a 10-base system can only be divided by 2 or 5. Not a problem today as we have calculators. The reason the 10-base system is used (mainly, although the imperial system is still widely used in some places) today is because we all should have 10 fingers and is easier and quicker to teach to children in an age where calculators do most of the work and education is effectively mass-produced, and speed is more important then quality.

Roman numerals are still widely used, it's true, but only on things like clocks and labels etc, not necessarily in maths because simply roman numerals are more limited (there still is no zero in roman numerals even today) and harder to use in equations. Writing a very large value in roman numerals can take up to 20 minutes, where as in modern maths we can use scientific notation, logarithmics and powers, it literally takes seconds to jot down a valve of several billions.

I used business in an earlier answer, because money talks loudly and it was actually business men who forced these numerals into modern day use. Not that they forced people to learn it or anything, but more that the business world started to adopt the system, because they could charge people more money, work out interest more accurately, and could keep track of expenditure better. As more and more business men used indian/persian numbers, they used roman numerals less, and everybody who wanted to buy or sell to businesses which used indian/persian numbers, had to learn to use them too. This had a snowball effect where more and more literate and business people learned and used the new numbers, eventually effectively abandoning roman numerals.

[M. Porcius Cato]

A decimal system is no more accurate than a base-12 system or a binary system. Think about it.

Yes your correct there but i thought were were talking about why 1234567890 came into use instead of I II III IV V VI VII VIII IX X etc.

Roman numerals are also as accurate as Arabic numerals.

[Neos Dionysos]

A decimal system is no more accurate than a base-12 system or a binary system. Think about it.

Yes your correct there but i thought were were talking about why 1234567890 came into use instead of I II III IV V VI VII VIII IX X etc.

Roman numerals are also as accurate as Arabic numerals.

 

They are, it's just easier to right 40 isntead of XL. Then again, perhaps we say that only because we grew up with the Arabic form and had we learned the Roman system, that would be much easier.

 

Though perhaps a better explaination is, while numerals are easier in lower forms, the Arabic is easier in much larger scientific forms... at least... from my viewpoint. I could be wrong.

[Sextus Roscius]

Think about it this way, to write one-hundred in arabic we put: 100-three digits.

 

Wheras the Roman Numeral system allows the to write: C-one digit

 

It makes sense if you think about it that way.

[eggers]

Think about it this way, to write one-hundred in arabic we put: 100-three digits.

 

Wheras the Roman Numeral system allows the to write: C-one digit

 

It makes sense if you think about it that way.

true, but how many times have you had to do a calculation where the answer is exactly 100? Although simple figures such as mulitbles of ten (1, 10, 100, 1000, 10000 etc) can easily be writen in roman numerals, maths is usually never that simple. Have you ever done a quadratic equation with roman numerals? no i haven't either, because i suck at maths, but rarely is the number exactly 10, 100 or 1000. Besides the romans never had zero so they couldn't do them anyway, but thats besides the point (quadratic equations = 0 before you start the boring task out working out the values).

someone wrote earlier that 3,888,888 = mmmdccclxxxvMMMDCCCLXXXVIII. How is that quicker or easier to write? try writing a number like 3,987,887,998,763,999 in roman numerals. Then times it by 334,009,732 and see if it's easier in roman numerals. We can do it today with long multiplication and express the answer in scientific notation the reduce paperwork. Its alot more complicated on a roman counting board.

There are quite a few reasons for the change from roman to arabic, writing large figures, equations etc, and after all that the system we use today must be better. Why would we use it today if it wasn't? You have to remember that change is difficult. Progress as a good thing is only a relative new phenomen (i can't spell, sorry! dyslexic). Before New ideas were often treat with suspion and more often hostility. The arabic numerals was heavily resisted when it first was introduced into Europe. "If it ain't broke, don't fix it" was the proverb of the day then. Afterall, they thought, we used Roman numerals for centuries just fine, why should we change? The romans built a huge empire, roads, the pathaleon, worked out taxes, the list goes on (although after the west roman empire dissappeared (for whatever reason) alot of people thought giants or gods built the aquaducts etc). Why should they change? the answer is simple. Arabic numerals are superior. They are more manuverable in equations, turns physics into a science, quicker to write, easier to teach. There is no conspiracy why they came in, and no-one bribed anyone i know to use arabic numbers. The simple fact is that they are here to stay because of the fact they are better to use. If roman numerals built the collossem, arabic numerals built sky-scrapers. If roman numerals built wooden triremes, arabic numerals built steel cruise ships.

[M. Porcius Cato]

The simple fact is that they are here to stay because of the fact they are better to use. If roman numerals built the collossem, arabic numerals built sky-scrapers. If roman numerals built wooden triremes, arabic numerals built steel cruise ships.

 

You're over-stating an already strong case. It's enough to indicate that arabic numerals include 0 and therefore allow an economical expression of a greater range of values.

 

To try to tie technology to numeric notation is a stretch. Using Roman numerals, for example, the total water delivered to Rome was greater than that delivered to New York City until around the 20th century, and the sanitary conditions in ancient Rome was greater than the level of that enjoyed today by about 1/2 of the modern (Arabic-numeral using) world's population.

 

Even in the history of mathematics and science, the discoveries of men like Archimedes and Euclid indicate that a non-Arabic system of numerals is not a serious impediment to progress. Obviously, great advances in mathematics have been made since the adoption of Arabic numerals, but I can't think of any that have been made BECAUSE people started using 37 instead of XXXVII.

[eggers]

Even in the history of mathematics and science, the discoveries of men like Archimedes and Euclid indicate that a non-Arabic system of numerals is not a serious impediment to progress. Obviously, great advances in mathematics have been made since the adoption of Arabic numerals, but I can't think of any that have been made BECAUSE people started using 37 instead of XXXVII.

 

True but archimedes and Eulid weren't using roman numerals. They use a system with the equivalent of 123456789 (greek symbols aren't here and i don't know how to import them) and they also had multiples of 10.

The size of atoms has been determined by maths, and they are incredibly small masses. I don't even want to go into the kind of equations used here, but using roman numerals would be a challenge. When the muslim scholar translated greek into arabic it wasn't don't for the fun of it. It was directly related to the mathematics they were using and the revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before or possible with roman numerals.

wow your really giving me a run for my money, ouch all this thinking hurts!

Edited January 26, 2006 by eggers