Comment by somenameforme | Hacker News Reader

Comment by somenameforme | Hacker News Reader

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Most people seem interested in this for mental math, but I think the correlation between Asia and mental math + abacus is spurious. All high level success in mental math comes down to is grinding/memorization, logic, and the knowledge of a handful of tricks. For instance somebody in this thread mentioned people finding impressive that they could multiply 42x37 in 10 seconds and attributed it to abacus work as a child. But this is really easy to do just using logic:

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Step 0 (plan) : We're multiplying 42x37. We need to find some simple (multiple of ten) numbers that are really close to the answer here, and then either subtract or add what's left over from our estimate. The most straight forward way to do this is to turn the problem into 42x40 - 42x3.

Step 1: 42 x 40 = 420 x 4 = 400 x 4 + 20 x 4 = 1600 + 80 = 1680

Step 2: 42 x 3 = 40 x 3 + 2 x 3 = 120 + 6 = 126

Step 3: 1680 - 126 = 1680 - 100 - 20 - 6 = 1580 - 20 - 6 = 1560 - 6 = 1554

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This process generalizes to basically any two numbers. And some otherwise scary sounding numbers make it really easy. For instance what's 87x99? It sounds hard but it's crazy simple because it's just 87x100 - 87 = 8700 - 87 = 8700 - 80 - 7 = 8620 - 7 = 8613, solvable in a second or two with practice. This is a 100% transferrable skill that will easily put you in the 'stupid human tricks' level of mental math - quite a fun 'trick' to have when teaching math!

I agree that multiplying 42x37 is not difficult. Many western mental calculators can do so quickly. I also agree that grinding, memorization, and tricks play a role in mental math.

> the correlation between Asia and mental math + abacus is spurious

However, I do not think the correlation is spurious. Involving additional brain areas like premotor (imagining moving the beads) and parietal (seeing the beads) is likely responsible for the incredible speeds achieved by trained abacus users. https://doi.org/10.1016/S1053-8119(03)00050-8

Western mental addition operates on fundamentally different timescales. Here's Aaryan Shukla adding 100 4-digit numbers in 300ms per number: https://www.youtube.com/watch?v=6ouUk0zIbos

That trick can be easily explained. All you need to do there is repeatedly add no more than 9 to 4 small numbers. Keep a running tally of the thousands, hundreds, tens, and ones places. Then at the end you re-add those numbers while obviously adjusting for overflow.

For a simple example: 1234 + 5678 + 9012. You get: 15 thousands, 8 hundreds, 11 tens, 14 ones. Now adjust for overflow (small to big): 4 ones (1 overflow moved), 2 tens (1 overflow moved), 9 hundreds, 15 thousands. Final calculation: 15,924. Notably the final 'adjustment' phase does not need to be done in 300ms, so all he's demonstrating is being able to repeatedly add 0-9 to 4 small numbers in 300ms. That's certainly an achievement and one that would require a lot of training, but nothing beyond that.

You can also see this in the video by his timing. The numbers start at 22 seconds and he finishes at 59 seconds. So he spent 30 seconds on the numbers (100 numbers at 0.3 seconds), and then around 6 seconds to input his answer.

I appreciate that you're demystifying this, but you are downplaying the difficulty of keeping 4 tallies with perfect accuracy for 100 steps while processing new inputs every 300ms. That produces demands on working memory and parallel processing that probably exceed the capabilities of our linguistic systems.

The claim is not that the algorithm is complicated, but that the abacus training helps in execution by involving visuospatial brain areas instead. Your argument is like saying training methods for track athletes are all equally effective because running is simply putting one foot in front of the other quickly.

You're simply describing unconscious competence - and there's no real secret to it besides lots of training in something. For instance you are unconsciously competent at reading. When you read the words I'm writing here you're not thinking at all - you just look at the text and the meaning instantly enters your mind. Yet think about all of the processing that somebody new to a language would have to go through - trying to recognize each letter in a word, combine those using whatever rules and quirks that exist in the language, think about the meaning of that word, and then repeat recursively to process a single sentence. The idea of being able to process 10 words a second (as a decent speed reader can) would seem superhuman, but it's not at all.

And how did you become unconsciously competent? By practicing reading and writing, a lot. FWIW you also probably have plenty of unconscious competence in mathematics as well. For instance what is 9x7? 63 probably enters into your mind with absolutely zero effort. Now what's 5x4? Again, it's the same thing. And in his situation it's made even easier because he knows what of the numbers will be to start with so it's like a series of 5x4, 4x3, 3x7, 7x2, etc. But the part you (and I) lack is the unconscious competence such that if we see 374 + 9, we have to think for that fraction of a second '374 + 10 - 1' to get 383, but instead need to see the answer literally instantly with no conscious thought whatsoever, and all that is is training.

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