Ancient Math

[mansamusa]

http://www.youtube.com/watch?feature=player_embedded&v=uXOTKidm7A0

 

 

base 1?

[imatfaal]

Well no - base 2. And needless sensationalism; desperately making it sound as if the ancient Ethiopian system is far better. The reason we use long multiplication with decimal figures is that within the the decimal system it is the easiest way to do long multiplication. It is natural to believe that the Ethiopian system is simpler because doubling and halving sounds easy - but when you are dealing with large numbers you need to think of it as multiplication and division by two, ie you need to do the maths"

 

I did 442*265

 

In the way I was taught; it was 9 single digit multiplications (with a few carry figures) and then three large numbers to add - the possibilities for error are there, but they are minimal. In the Ethiopian system there are 8 halvings (most very easy) and 8 doublings (most are not easy) and then an addition of three large numbers. I would choose to do 9 single digit multiplications rather than 33 multiplications by 2 every day of the week - and I think anyone who did this for a living as a book-keeper would too.

 

442

265

--------

2210

26520

88400

=====

117130

 

 

265 442 <--

132 884

66 1768

33 3536 <--

16 7072

8 14144

4 28288

2 56576

1 113152 <--

 

442

3536

113152

======

117130

 

Obviously both methods work - but I see the western version as 9 simple multiplications - whereas the Ethiopean is 8 much more complex multiplications

[SomethingToPonder]

Yes i agree, well put.