The Guardian‘s science section reports on a new numbers game, “Flash Anzan.” It’s based on the Japanese abacus, or soroban, which a million Japanese kids learn to use every year. The game requires mental representations of an abacus; the game, according to author Alex Bellos, goes like this:

. . . 15 numbers are flashed consecutively on a giant screen. Each number is between 100 and 999. The challenge is to add them up.

Simple, right? Except the numbers are flashed so fast you can barely read them.

Takeo Sasano, a school clerk in his 30s, broke his own world record: he got the correct answer when the numbers were flashed in 1.70 seconds. In the clip below, taken shortly before, the 15 numbers flash in 1.85 seconds. The speed is so fast I doubt you can even read one of the numbers.

Apparently they flash different sets of numbers at different rates, and the winner is the one who gets the right answer first at the fastest flashing rate.

Amazing. Here’s another clip,

. . . showing Sasano break the world record at 1.80 seconds. Note that the format of the competition is a bit like an arithmetical version of a spelling bee. The remaining contestants are sitting in chairs. The numbers are flashed. The contestants write down their answers and exchange papers for marking. The result is displayed on the screen, and those who got the correct answer stand up.

How does it work? Bellos explains more, but go over to his piece to see a bunch of other interesting stuff and one other amazing video in which the mental addition is done simultaneously with a word game.

Anzan was invented a few years ago by an abacus teacher, Yoji Miyamoto, who wanted to design a maths game that was only solvable by calculation with an imaginary abacus, a skill known as anzan.

When the contestant sees the first number he or she instantly visualizes the number on the imaginary abacus. When they see the second number they instantly add it to the number already visualized, and so on. At the end of the game the contestants cannot remember any of the numbers, or the intermediate sums. They only retain the final answer on the imaginary abacus.

Performing arithmetic using an imaginary abacus is the fastest way to perform mental calculations.

Startling what trained brains can do. A few years ago I reviewed Bellos’ fun book about math in the big world for my local paper.

Another interesting things was that in Japan, basic arithmetic facts are taught to children with songs (probably not unique in itself), and in order to expand the possibilities for good retention-building rhymes, some of the single-digit numbers have two different Japanese words. (Any Jap. speakers out there? When did this “synonymity” start?)

Also of interest, but maybe not so surprising in hindsight, was that a driving force for the pioneers of probability theory was success at the European gambling houses.

Then there was the story of the math genius who determined conditions under which it was favorable to purchase elebenty gazillion lottery tickets. He had investors, formed a company, and had some big wins.

On the different names for numbers, they are used to count different objects. The difference is in Chinese and is millenia old, I think. See here for more info on this very confusing aspect of Japanese language (it sometimes can confuse Japanese!): http://en.wikipedia.org/wiki/Japanese_counter_word

Put’s me in mind of the Speed Arithmetic method invented by Jacow Trachtenberg while he was in concentration camp. You have to work at it, but I remember multiplication by 11 being fantastically fast and easy.

Yes, it depends on the calculation. For sums it might well be true. However, nonlinear calculations, such as taking a cube root, are slow on an imaginary abacus and much faster with something like a mental Taylor series.

I just started an hour ago and can already do it (slowly)! And you can too!

I had no prior knowledge of the soroban and had to look soroban addition up on the internet. I have not looked up specific instructions on how to do the visualization.

The first thing I did, was to visualize only the pebbles that are out of their default position. I imagine the lower pebbles as connected chunks. That reduces visual clutter a lot.

It’s kind of amazing to be able to comfortably look and think about a second number, while comfortably holding the first one as a mental picture at the same time. This works presumably because different parts of the brain are used.

That means that I now have an accumulator register in my head, which is a basic necessity for any CPU or calculator.

The mechanics of the addition are easy to imagine.

So it is simple to start and I am sure that over time all of the transformations (arabic digit -> soroboan digit, arabic digit -> tens complement in soroban and additon) can be memorized by rote. First for one digit, then chunks of two, etc.

This should relly be standard teaching in all schools. I plan to develop this skill for practical use.

There are some reasons for why this might be close to optimal for the decimal system.

10 is only divisible by 2 and 5. The soroban breaks a decimal digit into a combined binary and a quinary digit, while maintaining compatibility with the decimal system at the same time.

There are lots of mnemonic device techniques to memorize numbers by shifting them out of your verbal system. But you can’t add an elephant to the eiffel tower.

In visual design there is the rule of seven. That is based on the notion that you can only perceive 7±2 items in a group before it gets confusing.

So you need a transformation that
.) frees up your verbal/symbolic system
.) maintains compatibility and interoperability with it
.) can be used for calculations
.) has manageable individual digits
.) but not too many digits to handle

It works extremely well in some cases until you meet someone who challenges you to do different calculations. Richard Feynman beat an abacus user by challenging him to calculate square roots.

## 20 Comments

I think my brain just broke.

That is fucking awesome.

My thoughts exactly

The result of academic freedom. If math were biology, that would be the work of the Devil.

Here is software for learning this method: http://figur8.net/baby/2011/04/18/math-secret-teach-your-child-to-do-math-faster-than-a-calculator/

Startling what trained brains can do. A few years ago I reviewed Bellos’ fun book about math in the big world for my local paper.

Another interesting things was that in Japan, basic arithmetic facts are taught to children with songs (probably not unique in itself), and in order to expand the possibilities for good retention-building rhymes, some of the single-digit numbers have two different Japanese words. (Any Jap. speakers out there? When did this “synonymity” start?)

Also of interest, but maybe not so surprising in hindsight, was that a driving force for the pioneers of probability theory was success at the European gambling houses.

Then there was the story of the math genius who determined conditions under which it was favorable to purchase elebenty gazillion lottery tickets. He had investors, formed a company, and had some big wins.

Fun book.

On the different names for numbers, they are used to count different objects. The difference is in Chinese and is millenia old, I think. See here for more info on this very confusing aspect of Japanese language (it sometimes can confuse Japanese!): http://en.wikipedia.org/wiki/Japanese_counter_word

You mean like this?

Its not

de riguerin the English-speaking world, but we do have them.Put’s me in mind of the Speed Arithmetic method invented by Jacow Trachtenberg while he was in concentration camp. You have to work at it, but I remember multiplication by 11 being fantastically fast and easy.

I can’t even visualize 796 as an abacus in 1.8 seconds, let alone add stuff to it.

It’s still easier than “Number Wang”.

I am SO relieved I wasn’t the only one thinking of Numberwang. (and Wordwang)

Yes, it’s time for wangon’on.

Let’s rotate the board!

Just don’t ask me to think of The Event. Remain indoors!

b&

“Performing arithmetic using an imaginary abacus is the fastest way to perform mental calculations.”

Citation needed.

Yes, it depends on the calculation. For sums it might well be true. However, nonlinear calculations, such as taking a cube root, are slow on an imaginary abacus and much faster with something like a mental Taylor series.

I just started an hour ago and can already do it (slowly)! And you can too!

I had no prior knowledge of the soroban and had to look soroban addition up on the internet. I have not looked up specific instructions on how to do the visualization.

The first thing I did, was to visualize only the pebbles that are out of their default position. I imagine the lower pebbles as connected chunks. That reduces visual clutter a lot.

It’s kind of amazing to be able to comfortably look and think about a second number, while comfortably holding the first one as a mental picture at the same time. This works presumably because different parts of the brain are used.

That means that I now have an accumulator register in my head, which is a basic necessity for any CPU or calculator.

The mechanics of the addition are easy to imagine.

So it is simple to start and I am sure that over time all of the transformations (arabic digit -> soroboan digit, arabic digit -> tens complement in soroban and additon) can be memorized by rote. First for one digit, then chunks of two, etc.

This should relly be standard teaching in all schools. I plan to develop this skill for practical use.

There are some reasons for why this might be close to optimal for the decimal system.

10 is only divisible by 2 and 5. The soroban breaks a decimal digit into a combined binary and a quinary digit, while maintaining compatibility with the decimal system at the same time.

There are lots of mnemonic device techniques to memorize numbers by shifting them out of your verbal system. But you can’t add an elephant to the eiffel tower.

In visual design there is the rule of seven. That is based on the notion that you can only perceive 7±2 items in a group before it gets confusing.

So you need a transformation that

.) frees up your verbal/symbolic system

.) maintains compatibility and interoperability with it

.) can be used for calculations

.) has manageable individual digits

.) but not too many digits to handle

It works extremely well in some cases until you meet someone who challenges you to do different calculations. Richard Feynman beat an abacus user by challenging him to calculate square roots.

One wonders how this guy would fare (if given abacus training :) )

www. youtube. com/watch?v=zJAH4ZJBiN8