From: nothing@invalid.com   
      
   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.   
      
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   --   
   Phil, London   
      
   --- SoupGate-Win32 v1.05   
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