Sunday, August 23, 2009

Still Clicking After All These Years

It’s difficult to know whether it’s appropriate to write about this, as it comes precariously close to sounding like I’m tooting my own horn, seeking some sort of public approval; that’s not my intention in writing this; rather, to encourage others to pursue their dreams, even if they take years to fulfill.

I have twenty-two of these little devices constructed, neatly arrayed in a plastic container. These aren’t rockets, and I’m no rocket scientist. Neither am I a finely skilled craftsman, although that’s what it would take to do a nicer job on these than I did. No, I’m a mere hack; but a clever hack, and managed, with marginal skill and meager tools, to fashion these little wooden devices, intended for the edification of a classroom of kids in a nearby town.

Today there are families of craftspeople in Japan who, having carried forth the tradition of their elders, and their elder’s elders, continue to fashion finely crafted soroban, the Japanese bead-frame abacus, using the same materials and similar designs of those crafted hundreds of years ago. These can be seen being operated by merchants and noblemen in classic Japanese artwork of the period. They are still being constructed and used today, and their benefits in accelerating the mental capacity of children are being more widely recognized.

How I ended up constructing twenty-two soroban in my workshop, for a teacher’s class in a small town in central New Mexico, is an odd tale, one of those that only happen in real life. I’ve recounted some of this in a previous blog entry, but perhaps rehashing the highlights is appropriate.

I happened upon the abacus while in high school, by fortuitous accident, having found a Japanese import shop that sold them, and also a classic book on the subject, written by Kojima. My personality fit well with anything unusual, odd or different – anything that no one else was into – hence the soroban was a perfect interest to take up.

I’ve continued my abacus interest, and basic operational skill, throughout my adult life. Several years ago I discovered a Yahoo discussion group on the abacus and through that group came into contact with a teacher in Socorro, New Mexico, a Taiwanese native, who was conducting a series of seminars at her school intended to introduce elementary school teachers to the abacus as the focus of an instructional program to supplement the normal math curriculum. I was invited to attend several of these seminars, during which I brought along several examples of abacus that I had built. One of the teachers at the seminar saw my handiwork and contacted me, inquiring as to the possibility of constructing a set of abaci for her classroom.

Over the years I had become interested in pursuing the design of a nine-bead abacus, a sort of modernization of the ancient Russian ten-bead abacus, as an alternative to the soroban, and as a result I had begun collecting various shapes and sizes of craft beads for use with the crude frames I was constructing. The problem of finding just the right size and shape of bead continued to haunt me, however. It seems that there really is no adequate substitute for the finely made biconic wooden soroban beads manufactured in Japan. I therefore made contact last year with a manufacturer in Japan and managed to secure a shipment of one thousand beads, at a cost of ten cents per bead. These things weren’t going to be cheap, but then again anything worth doing is worth doing right.

I had intended on using this shipment of soroban beads for making a few nicely crafted abaci for myself, but ended up just storing the beads away unused, as other issues became more important. And then one day I get a phone call from the teacher in Socorro, and the abacus project was suddenly on the front burner, and wouldn’t you know that those one thousand beads were just sitting in their plastic bag waiting to be called into service for a greater cause. I suppose it was meant to be, looking back on it now. Sometimes you can’t see the path forward until after you’ve broken through, and turn around to look back at where you’ve come from.

So, there they sit, these neatly constructed wooden frames with their uniform rods of diamond-shaped beads. I still have a few finishing touches to make before I can call them done. And then off they’ll go, like a whole litter of kittens being let go all at once, and perhaps for a few days I’ll feel a bit forlorn, like some empty nest syndrome, all that work and care and attention. But I must remind myself of that classroom of bright, young faces and eager fingers, and the tactile pleasure I first felt as a child when my fingers first clicked those elegant beads. Forty years later, they’re still clicking.

(Photographic note: don't attempt to portray your beloved handiwork under the harsh light of your shop's fluorescent light fixture. Incandescent or daylight would've been better.)

More background on my abacus pastime is appropriate.

This first image is the first 9-bead abacus that I constructed, back in the 1980s, and actually used in a TV repair shop to calculate repair bills. The round, plastic faceted craft beads were all I could find at the time; the alternating colors are useful in visually comprehending the size of number groups. Odd numbered groups (like 5 or 7) are characterized by the end colors being equal, while even numbered groups (like 4 or 6) are characterized by opposite end colors. This helps to overcome the primary disadvantage of the nine-bead abacus as compared to the 1:4 soroban, which is that the bead grouping sizes for numbers larger than four are more difficult to immediately comprehend. The advantage of the nine-bead abacus over the soroban is the lack of five's, and nested five's/ten's, complements problems; thus the nine-bead abacus is a good "starter" abacus for people just learning the concepts.

An example of a "nested complements" problem on the 1:4 soroban is 6+7, which requires a five's complement step be performed in order to complete a ten's complement intermediate operation (minus three is broken down into plus five, minus two). The nine-bead abacus only requires the ten's complement intermediate step (minus three, add a ten bead).

Oh, and the twenty columns of beads are not indicative of the over-priced repair bills at the TV shop(!); rather, when calculating sales tax (5.8125% at the time) required the subtotal be entered on one side, the tax rate on the other, and the cross-multiplication made on the middle rods. Later I figured out a shortcut for 5.8125%, which is 93/16, performed by: 1)multiplying by 100 -- done mentally by moving the decimal point 2 places; 2)multiply by seven and subtract from the subtotal; 3)dividing by 4 twice. This is much faster than multiplying by a five digit number.

This second image is a variation of the nine-bead abacus, with a different color scheme. Again plastic craft beads were used, round faceted in design. It's getting harder and harder to find abacus-acceptable craft beads at the big-box craft stores; these are about the only ones left from which to choose from. I also experimented with a 3-3-3 scheme of white-black-white; in the end I decided the original alternating design was best. You may also note in this model the prototype design of the "rod & lintel" construction method, which promises easier construction and an elegant design. I didn't use this method for the batch of twenty-two abaci constructed for the class in Socorro, as I thought they wanted a more traditional design.

This third image is the new "rod & lintel" construction method applied to a 1:4 soroban arrangement, using Japanese biconic beads. You'll notice the rods are of brass, and the cross-bar, rather than being a thin strip of laminated wood, penetrated by holes for each rod, instead is a piece of solid brass rod; this produces an interesting and unintended musical tone when swiftly flicking the beads back and forth. Perhaps I'll need to tune these abaci to some musical note? Also worthy of note is that this prototype is absent the decimal-place dots visible in the previous model; I would continue to use brass brads for this purpose in actual salable models. The lintels are of Brazilian cherry, the rods of black walnut. Going forward, were I to begin making these soroban for sale, this is the design I would prefer.

(Additional photographic note:
My Flickr account is approaching the 200-image limit for free accounts; thus I am uploading images to my blog direct from my computer, which are limited in resolution by Blogger itself; thus the small size and poor quality.)



Blogger deek said...

You, my friend, are one of a kind! I thoroughly enjoyed reading this today. It always amazes me how these connections come about.

10:52 AM  
Blogger speculator said...

I used an abacus in the darkroom, to count 4x5" sheet film duplicates- in complete darkness. I had my own decimal system for this, too. I hung the abacus on the wall, and put glow-in-the-dark tape on its edges. It was the best tool for that mundane part of the job.

12:07 PM  
Blogger deek said...

I was relaying my wife your story over lunch yesterday and she was very curious as to how an abacus works. Now I am too!

I've looked online and found a few resources and read up a little, mainly just addition and subtraction, which is fairly straight forward.

Two things: If you do plan on making any more soroban for sale, you've made me into a buyer. Second, are there good resources that you would refer. I find all this very intresting...math, my love for Japan and generally speaking, anything that can be referenced as a "throwback".

10:07 AM  
Blogger Joe V said...

For a good website on the abacus visit Totton's site at:

He also runs the Yahoo abacus/soroban discussion forum.

I'm not sure if I'll be making more abacus for sale in the short term, although that is a long term goal. I'll keep you updated on my blog if that changes.

Thanks for visiting.


10:52 AM  
Anonymous Dave said...

I've been teaching my 8-yo daughter multiplication and long division on a ten-bead, thirty-column abacus. I've mastered square roots, but cube roots are still a struggle for me.

The tenth bead isn't really necessary, but it simplifies the rules. Instead of "ten's complement of N", I say "move all but N beads". If I ask her to do a problem in another base, I drop in a fence that locks the unused beads out of sight, and the rules don't change.

My abacuses consist of pony beads on a string wound around a slab of foam core or masonite, all sold cheaply at Walmart.

Hint: It saves time and reduces errors to have a times table for any number you often multiply or divide by. For example, if your sales tax is 6.357 percent, write down

1 6357
2 12714
9 57213
10 63570 (to check your addition)

and keep it near the abacus. This method is also a handy crutch for users who haven't memorized the times table up to 9x9.

9:46 AM  

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