Counters

     After reading the blog post I wanted to know more about the make shift abacus merchants used to tally up totals of sales that was called a counter/counting board. I was very curious on what that would look like and how exactly it would work. I’ve heard of it before but only concerning the origin of the name and why we call counters in a business a counter. Looking into it more and being able to understand how it works must require knowledge of Roman numerals.

I=1

V=5

X=10

L=50

C=100

D=500

M=1000

     These are the basic Roman numerals. Another part before being able to understand how a counter works is to understand how to add and subtract Roman numerals.  When they are in a row like, XXX, that means you add 10+10+10=30. Or CLX would mean 100+50+10=160. If a smaller numeral is placed before a bigger one then that is where you would subtract. Like if you have IV, which would be 5-1=4. You can use those two rules to write a larger number in Roman numerals. If you want to write 971 you would first break it down to convert one digit at a time to make it easier. By doing this its actually using the Hindu-Arabic place-value number system that eventually replaced counters and Roman numeral methods. 

971

=900+70+1

=C-M+L+X+X+I

=CMLXXI

   When looking at a counter a merchant would use, it would have been made out of stone or wood. You would use pebbles or beads to count with by placing them in the columns, usually grooved so the pebbles/beads wouldn’t roll away. The size would vary between the size of a table down to the size of a portable abacus. 

                                            http://en.wikipedia.org/wiki/Counting_board

    

    The most simple counter would look something like this:

                                                                

                                                                       

                           All these examples of counting boards come from this site-    

                                   http://mathforum.org/dr.math/faq/faq.roman.html

     If a pebble was placed in the bottom part of the board it represented 1, 10, 100, or one 1000, all depending on its placement. If it was in the top part of the board it had its value multiplied by 5. So if a pebble was placed in column C, and C is 100, then its 100 x 5= 500.

                                   Example of what a number on a counter would look like.

     To decipher what this number is first break it down into steps. To write the number shown on the counter in Roman numerals you have to remember what values are represented by what numeral, if you cant remember the Roman numerals that equal 500, 50 and 5 (D, L, V) then just imagine the counter like this-

                                                                      D       L       V

     This number in Roman numerals would look like this- MMDLXIV. To decipher it into numbers it would be 2000+500+50+10+5-1=2564. This gets harder when the number gets bigger and more complicated, there can even be more columns added to hold bigger numbers. At that point in the middle ages most people actually turned the columns the other way and drew lines down the middle to accommodate more numbers being represented at once. Like this-

     For showing just the basic way they would calculate things, the vertical columns give a good depiction so it doesn't get too confusing. It took a long time to do these calculations the more complicated they got. So I'm sure it was a relief when people started switching from this method to the Hindu-Arabic numbers and calculation system, because it sure made things a lot simpler. 

These are the two sites I used to get information-

http://mathforum.org/dr.math/faq/faq.roman.html

http://en.wikipedia.org/wiki/Counting_board