On 2026-02-05 16:06, Paul wrote:

On Thu, 2/5/2026 4:19 AM, Daniel70 wrote:

On 5/02/2026 12:01 am, Graham J wrote:

John wrote:

[snip]

European alphabet-based languages were easier to learn.ÿ The only disadvantages was the Roman numbering system which was clearly a barrier to numeracy

I thought Roman Numbering was rather simple. at least for the lessor numbers.

OK, write a program to convert decimal integers to Roman Numerals :-)

Even better, write a program to multiply two numbers, up to one million,
in Roman numerals without converting to decimals. :-P

I accept doing it in paper.


--
Cheers, Carlos.
ES??, EU??;

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In article <10m4gn8$2sgi$1@dont-email.me>, daniel47@nomail.afraid.org
says...

But how much multiplication occurred in Roman Times?? Counting, sure,
one plus another one .... plus another one ....... plus another one,
sure, but Multiplication .... not so much!!

Interesting comment. It simply had to be wrong - trade and military
logistics would be impossible without multiplication (e.g. how to feed
an army of 10,000 for a three week campaign?). I put a query into an AI research tool (Gemini) and this is what it came back with:

The short answer is yes, they did a lot of multiplication?they had to
manage a global empire, after all?but they almost certainly didn't do it
"on paper" using the numerals themselves.If you?ve ever tried to
multiply XVIII by LXIV, you know it?s a recipe for a headache. Roman
numerals are an additive system, not a positional (place-value) system
like the one we use today. Because they lacked a zero and fixed columns
for ones, tens, and hundreds, the standard "long multiplication" we
learn in school is impossible with their notation.

Here is how the Romans actually tackled the math.

1. The Roman Abacus (The "Calculator")The most significant evidence we
have is the Roman hand abacus. Rather than scratching numbers into wax tablets, Roman accountants and engineers used a metal plate with sliding beads.How it worked: The abacus used a "bi-quinary" system (similar to a Japanese soroban). One set of beads represented units of five, and
another represented units of one.The Evidence: Several bronze hand abaci
have survived into the modern era. We also have literary references to
calculi (the small stones or pebbles used on larger counting boards),
which is where we get the word "calculate."

2. Duplation and Mediation (The "Egyptian" Method)There is strong
evidence that ancient mathematicians across the Mediterranean used a
technique called binary multiplication (also known as the Egyptian
method). This allowed them to multiply any two numbers using only the
ability to double and halve numbers.Example: 13 ? 11Halving (left side) Doubling (right side)Keep?1311Yes (Odd)622No (Even)344Yes (Odd)188Yes (Odd)Result: 11 + 44 + 88 = 143This method is perfect for Roman numerals because doubling a number like XVII to get XXXIV is visually intuitive
and doesn't require complex carry-over rules.

3. Finger Counting (Dactylonomy)The Romans were famous for a highly sophisticated system of finger counting that could represent numbers up
to 10,000.Instructional Evidence: The Venerable Bede (writing later, but reflecting Roman traditions) described how different finger joints and positions represented specific values.Utility: This wasn't just for
counting; it served as "mental RAM." A merchant could hold one part of a calculation on his left hand while working through the next part on his
right.

The Verdict

The evidence suggests that Roman numerals were for recording results,
not for performing the operations. Think of Roman numerals like a
"printed receipt." You wouldn't try to do math on the receipt; you use a calculator (the abacus) to find the total and then just write the final
number down. The fact that the Romans successfully built the Pantheon,
managed a complex tax code, and choreographed logistics for legions
across three continents is the ultimate "circumstantial evidence" that
their multiplication game was actually quite strong.

--
--
Phil, London

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On 2026/2/7 12:43:10, Philip Herlihy wrote:

In article <10m4gn8$2sgi$1@dont-email.me>, daniel47@nomail.afraid.org says...

But how much multiplication occurred in Roman Times?? Counting, sure,
one plus another one .... plus another one ....... plus another one,
sure, but Multiplication .... not so much!!

Interesting comment. It simply had to be wrong - trade and military logistics would be impossible without multiplication (e.g. how to feed
an army of 10,000 for a three week campaign?). I put a query into an AI

I was waiting for someone else to make this obvious point!

research tool (Gemini) and this is what it came back with:

The short answer is yes, they did a lot of multiplication?they had to
manage a global empire, after all?but they almost certainly didn't do it
"on paper" using the numerals themselves.If you?ve ever tried to
multiply XVIII by LXIV, you know it?s a recipe for a headache. Roman numerals are an additive system, not a positional (place-value) system
like the one we use today. Because they lacked a zero and fixed columns
for ones, tens, and hundreds, the standard "long multiplication" we
learn in school is impossible with their notation.

Here is how the Romans actually tackled the math.

1. The Roman Abacus (The "Calculator")The most significant evidence we

[]

2. Duplation and Mediation (The "Egyptian" Method)There is strong

[]

3. Finger Counting (Dactylonomy)The Romans were famous for a highly

[]

The Verdict

The evidence suggests that Roman numerals were for recording results,
not for performing the operations. Think of Roman numerals like a

[]
ISTR reading/hearing (don't know where) that they also _didn't_ use the pre-subtract notation - i. e. 4 was IIII, not IV; that was a later
invention (though obviously by someone still using "Roman" numerals).
I've seen a suggestion that it was actually invented by a clockmaker who
made a mistake when applying the numbers (put IV next to V on the wrong
side, rather than where VI should be); I'm dubious about that idea (and
no idea where I heard it either). It _is_ noticeable that a lot of
clocks _do_ use IIII rather than IV, though.

--
J. P. Gilliver. UMRA: 1960/<1985 MB++G()ALIS-Ch++(p)Ar++T+H+Sh0!:`)DNAf

Some cause happiness wherever they go; others, whenever they go.
- Oscar Wilde

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