What Good Are Roman Numerals?

MayCaesar

Depends.

What is 10 + 3? 13.
What is X + III? XIII.

How many digits does it take to write a thousand in the Arabic format? 4.
In the Roman? 1.

The Roman numerals, should you get used to them, actually work very well when it comes to relatively small numbers (the numbers that concerned the Romans at the time, for instance). They are not ideal when talking about things like the number of atoms in the Universe, but they do not appear to me to be significantly less efficient than the Arabic numerals when it comes to everyday calculations. The Arabic numerals are universal (in that you can write any conceivable integer number with them), but the small Roman numbers are a little more intuitive (they are more akin to how children count).

John_C_87

They are written with letters and no additional education or training is required for writing...

John_C_87

Did you know that Roman Numerals used a duodecimal system rather than a decimal system of fractions based on tens.

JulesKorngold

Argument Topic: A Challenge

@MayCaesar
Multiply MMXXIII by XXVII and show your work.

Barnardot

@JulesKorngold

Multiply MMXXIII by XXVII and show your work.

LIVDCXXI

I dont really want to show my work because you wouldn't want to see chickens getting knocked off.

JulesKorngold

Argument Topic: Totally Wrong

@Barnardot
Not even close.

John_C_87

@JulesKorngold

SNI 
There is no work you are asking to multiply 3 x 7 and it equals 21....
I understand you may have been looking to write 2023 multiplied by 27. The attempt is to use the Vinculum system or some other additive form of Roman numerals. I personally like to just break off and use additional values added from the Middle Ages. Hence the letters (SNI) for the number 21 which can be written as (OX) While the duodecimal system accounts for the idea of I - XII on a clock the start of the mathematical reasoning behind natural numbers in mathematics for geometry reasons. Two of the same letters used side by side can mean zero so II = 0, XX = 00, and CC = 000

JulesKorngold

Argument Topic: Still Waiting

@John_C_87
So what's the answer in Roman Numerals?

just_sayin

I see Roman numerals used most frequently in long government documents and scientific papers.  It helps to break up the subsections so you can know where you are in the document.

MayCaesar

JulesKorngold said:

@MayCaesar
Multiply MMXXIII by XXVII and show your work.

Happy to. I will use the bold symbols in place of overlines, like so: X = 10,000. Any symbol in bold equals to corresponding number of thousands.

1. Decompose the first term: MMXXIII = (M + M) + (X + X) + (I + I) + I = (M+X+I)*II + I
2. Decompose the second term: XXVII = (X + X) + V + (I + I) = (X+I)*II + X/II
   
3. Therefore MMXXIII * XXVII =  (M+X+I)*(X+I)*II*II + (X+I)*II + (M+X+I)*X + X/II = [M*(X+I) + X*(X+I) + (X+I)] * IV + (X+I)*II + (X + C + X) + V = [X + M + C + X + X + I] * IV + (X+I)*II + (X + C + X) + V
   
4. Counting how many times each term appears, we get: MMXXIII * XXVII = (X * V) + (M * IV) + (C * V) + (X * XI) + (I * XI) = M * (X * V + IV) + (C * V + XI * XI) = M * (L + IV) + (D + CXXI) = LIVDCXXI

We can verify the result with Arabic numbers. MMXXIII = 2023, and XXVII = 27, and 2023 * 27 = 54,621

In our result:
LIV = LIV * M = 54*1000 = 54,000
DCXXI = 500+100+21 = 621
LIVDCXXI = LIV + DCXXI = 54,000 + 621 = 54,621

Happy to elaborate on any of the steps.

John_C_87

@JulesKorngold

There is more than one answer, and multiple answers cannot be written in one set of Roman Numerals and is best written in a combination of medieval abbreviations from combination of the Middle Ages Renaissance, and Roman numerals. I wrote the first answer down already which is SNI 7 x 3 = 21 in MA, R, & RN letters can be (SNI) or (OX) = 21 though can be written as XXIII in a simplistic way. The issue is that with roman numerals it might be written with 5 leading zeros’ like 00000III due to the use of abacus. 

JulesKorngold

Argument Topic: Impressive!

@MayCaesar
Please elaborate the steps you took to multiply 2023 by 27 using Arabic numbers.

Which process is easier? Roman or Arabic?

What about dividing 54,621 by 2023?  Which process is easier?

John_C_87

@MayCaesar

1. Decompose the first term: MMXXIII = (M + M) + (X + X) + (I + I) + I = (M+X+I)*II + I
2. Decompose the second term: XXVII = (X + X) + V + (I + I) = (X+I)*II + X/II
   
3. Therefore MMXXIII * XXVII =  (M+X+I)*(X+I)*II*II + (X+I)*II + (M+X+I)*X + X/II = [M*(X+I) + X*(X+I) + (X+I)] * IV + (X+I)*II + (X + C + X) + V = [X + M + C + X + X + I] * IV + (X+I)*II + (X + C + X) + V
   
4. Counting how many times each term appears, we get: MMXXIII * XXVII = (X * V) + (M * IV) + (C * V) + (X * XI) + (I * XI) = M * (X * V + IV) + (C * V + XI * XI) = M * (L + IV) + (D + CXXI) = LIVDCXXI

This isn't correct...
To be honest JulesKorngold I don't have it in me to do the work in a outside program and bring the image in....sorry I give MayCaesar credit for even trying to do the work long hand in the forum limitation...His end game answers is right. 

Barnardot

@JulesKorngold ;Not even close.

Yes thats because its spot on and if you really want to see my working out all you need to do is click a couple of times on google and any dufis can do that so why get so tarded and old fashioned and try doing things the hard way. You see smart people do things the easy way.

MayCaesar

JulesKorngold said:

@MayCaesar
Please elaborate the steps you took to multiply 2023 by 27 using Arabic numbers.

Which process is easier? Roman or Arabic?

What about dividing 54,621 by 2023?  Which process is easier?

I am sorry, but I am not going to keep answering these questions requiring a lot of work without you reciprocating my efforts.

As far as which process is easier, for me it is much easier to work with Arabic numerals because that is what I have done my entire life. Had I instead worked with Roman numerals all this time, it would be the opposite. Roman and Arabic numerals are based on different internal logic and have different advantages and disadvantages. One of the Roman numbers' advantages is ease with which one can work with halves (and that is illustrated in my solution: look at how naturally everything comes together in step 4), without the need to explicitly divide the number by two (for instance, C / II = L, which is much simpler to write than 100 / 2 = 50). Arabic numbers, on the other hand, are easily scalable as everything can be naturally written as a sum of powers of 10 with small factors.

Both systems are suboptimal and somewhat arbitrary compared to some of the alternatives. It would make more sense, for instance, to not use 10 as the base for Arabic numerals, but a sufficiently small power of 2. 32 would work quite well as 32 = 2 * 2 * 2 * 2 * 2, and it is much easier to convert it to the binary format and back which is quite relevant in the digital world we live in - and we, in fact, could easily switch to this format without introducing any new symbols by supplying digits from 0 to 9 with English letters. Similarly, Roman numerals could be made much more efficient if they generalized division by 2 to division by powers of 2, so, in addition to C / II = L we would also have C / IV = *one symbol* and so on.

The more you use a given system, the more "tricks" you learn that help you simplify the calculations. At some point, during my undergrad years, I could multiply any 4-digit integer by any 4-digit integer in my head, and that heavily relied on the pattern recognition - and that recognition only comes with having found those patterns by working out operation after operation. Spend a few years working with Roman numerals, and you will learn a lot of tricks that do not apply to Arabic numerals. How do you think brilliant Ancient Greek mathematicians did their calculations with the system on which Roman numerals were based on?

John_C_87

@MayCaesar
Roman Numerals had been meant to work with a custom Abacus or custom calculator the custom Abacus being easier to create or have built. The reality here is that there is no need to show the work like with algebra as many of the rules of algebra do not apply to Roman Numerals.

 @ JulesKorngold

Remember the Roman numeral system is based on duodecimal system and regulated decimals like 1/4 and 1/3