[codehotter]

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.

[somenameforme]

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.