(If you haven’t read part I you might like it too. Go ahead. I’m waiting.)

The book was a good start but I was looking for something more original. While my friend is a programmer, and a good one at that, she’s actually a mathematician at heart. So I started looking for a fitting gift to appeal to that part of her.

At first I thought I’ll be able to find a replica of the Curta calculator for a reasonable price. The Curta calculator has an interesting story that dates back to the concentration camps in WWII. You can see how amazing it is in this video:

Unfortunately, the Curta calculator is only available as a collector’s item and can be found on eBay starting at about 600$ (if you’re lucky.)

In the spirit of used stuff (like the book I got in part I. Told you to read it) I decided to try and look for an antique abacus. In the process I learned quite a lot about the history and evolution of abacuses, which is really interesting. The most “advanced” one, for example, is Lee Kai-Chen’s abacus, which allows you to do complicated operations like finding the square root of a number and more. Unfortunately, those are extremely rare and I couldn’t find any. What I did find was this amazing video on children using the abacus:

That last part about “mental calculation” really surprised me.

While looking for a nice-looking abacus on eBay I stumbled upon the perfect gift – a Klein bottle. A Klein bottle is a mathematical shape with interesting properties – it only has one side and zero volume (Here’s a Wikipedia link, in case you’re into this sort of stuff.) And the gift is perfect not just because it’s great for a math-oriented person like my friend. It’s perfect because of the experience I had getting it. Little did I know, when I purchased a medium sized Klein bottle from kleinbottle.com, that I will be getting the following response from the seller, Cliff Stoll:

Dear Amit,

Thank you very much for your Klein Bottle order! I’ve just snuggled the Medium Classical Klein Bottle into a 23x15x15 cm box with plenty of bubblewrap & padding, as well as the usual Acme literature, invoice, and agitprop.

While packing the Klein bottle, I took a few photos. You can see these pictures at

http://www.kleinbottle.com/gallery2/main.php/v/455SomePhotosForAmitAbout half an hour ago, I bicycled to the Post Office and sent the box via Express Mail International. The box should arrive in a few days depending on the post and Israeli customs.

The postal tracking number is ECXXXXXXXXXUS. Within a day or two, this tracking number should show up on the US Postal website, http://www.usps.com/shipping/trackandconfirm.htm

So from across the Atlantic and around our three spatial dimensions, here’s my warm cheers to you … I’m sure you’ll like the Klein bottle!

– Cliff

And here are the pictures I got from Cliff:

The pictures were a stunning personal touch. I was so happy about getting this kind of customer service and wrote him back a thank you note with a link to the pictures from my latest trip.

It soon became obvious from our correspondence that Stoll is not your regular bottle maker so I looked him up. It turns out the bottle making was a secondary venture of a well known astronomer and mathematician. Here’s his Wikipedia entry, but even a Google search for Cliff Stoll brings up interesting results, including this TED talk:

To come full circle with this post it turns out Stoll is a fan of the Curta calculator. Here’s a video of him telling the story of the calculator and how its inception saved its creator:

Hmmmm,

When I was a child, and even (slightly) geekier than I am today, I learned to use a Japanese abacus that my father brought from the US at some point. It came with a little booklet explaining how to use it.

It’s surprisingly easy to learn, and I mastered it in a few short hours. I obviously didn’t get to this “mental” type of calculation shown in the video, as the booklet said nothing of it, and I strongly suspect that the whiz-kids who do this in the video have a very special “gift” or “knack” for it anyway – Normal people will probably not be able or indeed willing to learn this…

The booklet did have a lot of “motivational propaganda” saying that the abacus is much faster than an electronic calculator. My own timings, after a few hours of practice, indicated a very close tie. I suspect that with some more practice the abacus would have indeed won. Of course, this is just for addition and subtraction, especially with a large number of terms. The abacus is quite pathetic with any other operation (except, of course, multiplication by zero, which is the fastest).

The thing that did surprise me mentality-wise is that while you are doing the calculations you don’t have to think about the math at all. You just follow a set of easily learned, almost “robotized”, finger movements for every combination of figures.

AFAIK, there are 2 other types of abacuses in common use (the one shown in this post is the Japanese type): The Chinese type, which is similar, but slightly more elaborate, and the Russian, which is just a set of horizontal wires with 10 beads on each – very similar to the abacus toys available in the better toy shops. My grandfather used to have a Russian abacus in his office, and according to stories, actually used it regularly. AFAIU, both the Chinese and Russian types are less minimalistic and therefore less efficient.

And don’t get me started on slide-rules…

:) Thanks a lot for the reply. I actually went on a hunt for an authentic (old) abacus, but they sell all these crap ones. And the most interesting one, the Lee Kai-Chen’s abacus, which can be used to do square roots and such, isn’t available anywhere AFAIK.

There’s also the relatively famous “Feynman vs. The Abacus” ( http://www.ee.ryerson.ca/~elf/abacus/feynman.html )story from a book that I really like about Richard Feynman (a famous physicist from the 20th century.)

Anyway, I gave up on trying to find an abacus. I still follow Curta calculators on eBay though, in case I’ll get lucky and find one relatively cheap.

Thanks again.

Hi, as usually i forgot my user and pass… As usual, the gift is very original and based on great ideas. So, did she like the gift?????

She liked it a lot! Probably one of the most successful gifts I’ve ever given.

The story that came with it was a great addition. I actually enjoyed looking for and giving it.

(Next time we meet I’ll reset your password :)

You can calculate square roots on any abacus or soroban, digit by digit, with relative ease. Write me if you need a description of the algorithm.

The Lee Kai-chen ‘Improved’ Abacus is rare and hard to come by indeed. This is to let you know that the Lee abacus is available to anyone who owns an iPad. The app is called AbacusPro. The app includes two versions of the Chinese Suanpan, the Japanese Soroban, and the Lee Kai-chen ‘Improved’ abacus.