Abacus is alive and well. Really, really well...

[Delta4Embassy]

World s fastest number game wows spectators and scientists Alex Bellos Science theguardian.com

"And the high point of the championship is the category called "Flash Anzan" – which does not require an abacus at all.

Or rather, it requires contestants to use the mental image of an abacus. Since when you get very good at the abacus it is possible to calculate simply by imagining one.

In Flash Anzan, 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.

I was at this year's championship to see Takeo Sasano, a school clerk in his 30s, break 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.

...

"When I returned to London, I met up with Brian Butterworth, professor of cognitive neuropsychology at University College London and the author of The Mathematical Brain, and showed him some video clips of Flash Anzan.

He was flabbergasted. "I don't see how you can represent whatever that number was on a mental abacus faster than you can say it," he said, adding: "A lot of money should be spent doing research on how the brain can manage to do this, because I think this is a really extraordinary thing!""

It's one of those reasonably fair stereotypes Asians excel at math. And maybe this is why.

 

[The2ndAmendment]

Excellent video.

They should also teach certain critical thinking tricks to accelerated math students in our own high schools that would get them thinking. What's 91 x 89? Obviously it's 8099, (x-1)(x+1) = x^2 - 1, let x = 90, 90^2 -1 = 8099.

You may think that's a "one trick pony" but if someone asked me what 53 x 49 was, I'd instantly think:

(x+3)(x-1) = x^2 + 2x - 3

Let x = 50, 2500 +100 - 3 = 2397. I'll admit, the first answer that came to mind was 2403, because I added 3 instead of subtracted, but that answer was nearly instant, under a full second

Try 78 * 62. (x+8)(x-8) = x^2 - 64. x = 70, 4900 - 64 = 4836. This took me about 2 and half seconds to calculate in my head.

Just as the children claimed in that video, I am NOT doing the raw calculation. I'm playing games with a system I excel in (multiplying binomials), just like they are with an abacus.

---------------------------------------------
What is 635^2? I will treat this as :

Step X (630 + 5) ^2 = x^2 + 10x + 25, x = 630. The sum of 10x + 25 = 6325. , so the only part I actually need to calculate is 630^2. This is simply 63^2 with two zeros on the end of it.

Step Y
63^2 = (60 + 3) ^2 = y^2 + 6y + 9; y = 60, = 3600 + 360 + 9 = 3969, put two zeros on the end, 396,900.

Step X repeated (for me personally)
In my head I have to recalculate 10x + 25 since it shorts out of my memory, but I get 6,325 in under a second. I make sure to "burn the image of the commas into my brain" so i can complete the final step of adding 396,900 + 6,325
(Step Z) This "burning the comma in my mind" is very similar to the abacus, which relies on locations, the comma is a location.

I know this operation will roughly carry a one once or twice, so I'm already mentally prepared for it. I calculate the first three digits: 225, then the last three digits: 403

403225

Step A takes me under two seconds.

Step B takes about 5 seconds.

Step A recalled takes under 0.5 seconds.

Step Z takes 11 seconds. Yes, raw adding is actually one my weaknesses. It will take me roughly 15-25 seconds to complete the square of a 3-digit number (it takes 2-6 seconds for 2-digits numbers). This particular number was moderately complex because the digit 6 keeps appears in every calculation, except the final one, which juggles and scrambles the locations of all the 6's in each location, forcing me to recalculate Step X.
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Anyway, if they taught mental math tricks like this (or any others would be cool too), the kids would be generally smarter, like those Asians and Indians using the abacus.

 

[Delta4Embassy]

Excellent video.

They should also teach certain critical thinking tricks to accelerated math students in our own high schools that would get them thinking. What's 91 x 89? Obviously it's 8099, (x-1)(x+1) = x^2 - 1, let x = 90, 90^2 -1 = 8099.

You may think that's a "one trick pony" but if someone asked me what 53 x 49 was, I'd instantly think:

(x+3)(x-1) = x^2 + 2x - 3

Let x = 50, 2500 +100 - 3 = 2397. I'll admit, the first answer that came to mind was 2403, because I added 3 instead of subtracted, but that answer was nearly instant, under a full second

Try 78 * 62. (x+8)(x-8) = x^2 - 64. x = 70, 4900 - 64 = 4836. This took me about 2 and half seconds to calculate in my head.

Just as the children claimed in that video, I am NOT doing the raw calculation. I'm playing games with a system I excel in (multiplying binomials), just like they are with an abacus.

---------------------------------------------
What is 635^2? I will treat this as :

Step X (630 + 5) ^2 = x^2 + 10x + 25, x = 630. The sum of 10x + 25 = 6325. , so the only part I actually need to calculate is 630^2. This is simply 63^2 with two zeros on the end of it.

Step Y
63^2 = (60 + 3) ^2 = y^2 + 6y + 9; y = 60, = 3600 + 360 + 9 = 3969, put two zeros on the end, 396,900.

Step X repeated (for me personally)
In my head I have to recalculate 10x + 25 since it shorts out of my memory, but I get 6,325 in under a second. I make sure to "burn the image of the commas into my brain" so i can complete the final step of adding 396,900 + 6,325
(Step Z) This "burning the comma in my mind" is very similar to the abacus, which relies on locations, the comma is a location.

I know this operation will roughly carry a one once or twice, so I'm already mentally prepared for it. I calculate the first three digits: 225, then the last three digits: 403

403225

Step A takes me under two seconds.

Step B takes about 5 seconds.

Step A recalled takes under 0.5 seconds.

Step Z takes 11 seconds. Yes, raw adding is actually one my weaknesses. It will take me roughly 15-25 seconds to complete the square of a 3-digit number (it takes 2-6 seconds for 2-digits numbers). This particular number was moderately complex because the digit 6 keeps appears in every calculation, except the final one, which juggles and scrambles the locations of all the 6's in each location, forcing me to recalculate Step X.
-----------------------------------------------------------------------------------------------------------------------

Anyway, if they taught mental math tricks like this (or any others would be cool too), the kids would be generally smarter, like those Asians and Indians using the abacus.

(drifts off thinking of bikini clad girls..) Huh? What?

I hated math in school yet ironically do a similar function in my head for arithmetic. I dunno how they teach is typically now, but fact remains US sucks at math, science, and language in global rankings. So something needs to change. And since Japan and China usually hold the top 2 in a death grip, adopting whatever they're doing seems the way to go.

 

[jasonnfree]

Thank everybody for these posts and threads on math, computers, etc. I still have an abacus from Japan when I was there in '65. I learned it and also the Korean chisenbop system for fun.I won't let my 10 year old great grand kid who I'm raising, use a calculator. I'm being a hard ass on him making him pencil everything. A little earlier I tried 2nd amendment's using binomials and squaring numbers to multiply larger numbers, took awhile to understand it , I'm still slow and rusty at mental calculation, but I like it. This is what our kids should be doing in schools I'm in agreement.