On Mon, Feb 21, 2011 at 09:34:07PM -0500, [email protected] wrote:
>
> Have you ever noticed that an abacus has unnecessary beads?
>
> After the "one" counters get up to four the next "one" makes it five and you
> zero the five "one" beads and move a "five" bead over. The fifth "one" bead
> is
> not needed because once it is moved the "one" row is zeroed.
>
> Same with the second "five" bead.
Actually, for the Russian and the Chinese abaci (which are the ones that
I know), that 5th bead has a very important purpose. Working the abacus
is not simply a matter of moving and counting the beads: it's a
visualization tool that allows you to build muscle memories for using it
- i.e., to "mechanize" its operation so you can use it without thinking
about the process. The _result_ of that operation is a very fast
tabulator - but the _mechanism_ by which that tabulation happens is
based in large part on the tactile distinctions in the small set of
beads on each wire as well as the ability to "snap-shoot" the results
visually.
Please note, by the way, that abacus use is still taught in a number of
schools around the world: abacus visualization, even without having a
physical one at hand, allows you to perform mental math at many times
the normal rate when large, complex numbers are involved.
When I was a kid, there was no other device available to us average
humans for calculating numbers (sure, the big university in Moscow had
some kind of an electronic machine, but no one else did!), and so
everyone, including accountants, used a total of two tools: mental math
and abaci (well, paper techniques too, sure - but that's more or less
standard.) No matter how complex the organization was, that was always
sufficient.
Once you're used to it, doing math on the abacus is a lot faster and
more accurate - and in the case of a large list of numbers, dozens if
not hundreds of times faster while maintaining that accuracy - than
doing it on paper. In fact, I would put a professional abacist against
anyone with a calculator or a computer for addition and subtraction -
and possibly for multiplication and division as well. Square roots to,
say, three decimal places, a little slower. Cube root, a good bit slower
but still within a few seconds. The point is that these are all doable
on a device a couple of thousand years old - matched against the latest
achievements of science. Sure, a computer is much faster at figuring out
the arctangent of 0 / -1 to 50 decimal places... but very few people in
this world need "pi" to that level of precision (never mind that most
computers actually can't do it anyway - not with any standard tools
available to the layman, or even to most programmers. Integer math isn't
a computer's strong suit, the poor things. [grin])
Again, those beads are necessary because the point of an abacus is to
make operations as fast and as intuitive as possible... and we humans
don't count too well by fours. With fives, a single visual pass over a
set of rows will give you a nearly instant answer with minimal
calculation; it's not "5 + 50 + 500 + 5000 - 20 - 3"; it's more like
"all except 2 here and 3 there: 5532". It's hard to imagine how fast and
convenient that is, and how, when coupled with the tactile end of it, a
professional can calculate with one hand without even looking at it, and
so can write the result with the other hand.
Unfortunately, this is all 35 years or so behind me, and I couldn't even
begin to do any useful work on an abacus today. My mental math skills
have also deteriorated to a tiny percentage of what they once were (and
that was at the ripe old age of 13.) Even so, I'm often shocked by
people being amazed at how quickly I can calculate certain things... to
me, that's just "natural", simple math, and something that "everyone
just knows". Except not. Which is actually pretty awful, now that I
think about it. Math, like chess, is a great tool for maintaining mental
acuity no matter how old you get, and losing it - or not having it in
the first place - is an absolutely terrible thing.
But that may just be my outdated viewpoint.
Ben
--
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