this is a set of Napier's bones which were invented in the early 1600s they're used for
multiplying with a big number each stick has a number at the top along with nine
rows numbers arranged in triangles. There's the special stick called the
index rod which just has all the digits one through nine in order
unlike a lot of things in mathematics Napier's bones were actually named after the person who
actually invented them john napier. napier was a Scottish nobleman who's best known for inventing
the logarithm. he computed and published the first book of logarithmic tables which also happened to
be the first major work to write numbers using a decimal point. napier invented logarithms which
eventually led to the invention of the slide rule but Napier's bones actually had nothing to do with
logarithms or slide rules. the bones give you the exact answer when you want to multiply a large
multi-digit number by a single digit. here's how you do it it looks a bit magical. let's multiply
7 times 240,983. first you line up the bones like this the index rod goes on the left and
then you put the other rods in order spelling out your big number across the top so I want to 2 4 0
9 8 and then 3. now I look at 7 on the index rod and I look across the bones just in that row and
as you look across you add numbers up diagonally. so we got one here then 2 plus 6 is 8 then three
plus five is eight again then a 6 + 8 + 2 + 4 6 and then this one here and that's the answer.
really that is the answer you can check it if you want. here I'll check it on my calculator
see that it's a calculator. I bet you thought I was going to... but this but this is a calculator
the burroughs calculator because I like the old I don't like the new but i like calculator.
I'm just going to just do Actually this is based on a method
of multiplication called lattice multiplication. Here's an example if I want to do 25 times 43, the
way I learned when I was a kid looks like this. Actually when I was a kid I didn't write exactly
this way but I'm splitting out a few steps so we can see a bit more clearly. You do the 5
times 3 is 15 and then the 2 times 3 is 6 but you offset it over here and then give
you 4 times 5 that's 20 and then 4 times 2 is 8 and then you add all these up and you get 1075.
The lattice multiplication would look like this you write one number vertically and
one horizontally so there's a 25 and the 43 and then you make a little grid that's the
lattice. And in each grid spot you write the product of those single digits so here I do 4
times 2 is 8 here 4 times 5 is 20 buh buh buh. And then you put these little diagonal lines
in and you stick in zeros if you need to. And now we add up diagonally going down I
get 5 over here and then 0 plus 6 plus 1 is 7 here and then 2 plus 8 is 10 here and that's
my answer. It looks totally different than the way I learned it in school but if you put them
side-by-side you'll see it's really the same thing it's just rearranged. See the answer is
still being computed as a 5 over in the rightmost digit and then a 1 plus 6 plus a 0 in the middle
and then 2 plus 8 gives you 10 on the left. Here's another lattice example let's try 7 times
240,983 which is what we did on the bones before. The lattice this time has just a single row and
it looks like this. Looks familiar doesn't it? See the numbers on the bones are the same as
the ones that appear in the lattice that's why the bones gives you the right answer. The bones
seem like a novelty today but they were actually a bit of a revolution when they were invented.
Before the bones the only real computational device was the abacus.
In fact the bones are sometimes referred to as rod abacus not because it works like an abacus
but people just had no concept of a physical device for computation except for the abacus.
But for the specific task of multiplying a big number by a single digit the bones are
much much better than an abacus let's try my old example seven times 247,983 on an abacus.
I mean use my Russian abacus lucky for me it's got a lot of digits you need one row
of beads for each digit so a smaller abacus would fail on this computation right away.
Now I'm not very good at using an abacus so I hope you'll forgive me if I do it kind of slowly.
I'm going to say out loud all the stuff that I have to do in my head as I go.
I go seven times three is twenty-one. Seven times eight is fifty-six up here. Seven
times nine is sixty-three up here. Seven times zero is zero in this digit. 7 times
4 is 28 up here. Seven times two is fourteen. This is not really easy you have to remember
the numbers that you're working with in your head as you're doing it plus you have to do a
bunch of mental multiplying at the same time and you also have to move little beads around which
is hard unless you'd practice a lot. I had to re-record this several times
because I kept messing it up. Some people would practice
hard to become really awesome on the abacus. But even a fool like me can easily use the bones.
So the bones is a great improvement over the abacus and it's pretty fun to use today.
It's also really easy to make your own set I'll show my complete set here if you want to make one.
Just copy the numbers that I have and make sure they all line up right.
I made mine with a sharpie on the back of home depot paint
sticks. Ask the paint person nice and they'll give you some for free. They
get suspicious giving out lots of them at once so make a few trips.
I'm here to start some static about money murder and mathematics.