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:
-----
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
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.
I've got a soroban but never got around to learning it. Definitely should pick that up again.
When I was at Uni (electrical engineering) I noticed that the Chinese students would reach for their calculator way less than western students and assumed that was because of the abacus.
Side note: they tried to shape a control theory subject (everyone was getting 100%) by disallowing calculators in tests. It was rough having to do things like long division for the first time in decades. Still everyone got 100% haha.
Author here. Very surprised to see this on HN years after I stopped!
Also, thanks for the UI critique, points taken! The design decision was to hide nitty gritty detail about the background unless the reader was extra interested, in hopes of making an article with gradual / adjustable depth so readers who aren't as interested can get a tl;dr for each section (I still don't know how a nice UI to do this, although LLMs make the idea more in reach now).
I love this idea for how we could have dynamic LoD for articles. I've thought about this a lot over the years and also never landed on a great ux. Maybe llms will help us; it would be great to see these tools shape novel, powerful ux (in the hands of the people).
Thanks for your articles. About your "The surprising benefits of disciplined, deliberate self-logging", I couldn't understand and it seemed cryptic how you're logging? The biologger.md is throwing 404. Could you explain?
Wow, thanks for digging! Looks like I haven't committed that file! It's an incomplete description of the android app that I wrote to output the jsonl in the self-logging piece going through some comparisons of existing options in 2019 and design decisions for the app. In short, it's like myfitnesspal tailored to my use case. 3 years later, the data is still a sprawl, but the logging strategy is stable.
Why the custom computer keyboard? Why not practice on a real soroban? They cost about US$10. You need to practice the finger motions, after all. They're not bad for addition and subtraction. For adding up small numbers, such as at a store checkout, a soroban is still useful. Multiplication, division, don't go there.
With a soroban and a slide rule, you can do most basic engineering problems.
I wanted to track my progress to the highest level of detail possible. The motor motions are somewhat similar, but slightly more complex, than typing on the keyboard. But since I already type fluently I wouldn't be able to get as fresh data, so the soroban was a nice other task.
The main goals were to track learning progress and truly experience what it meant to have a virtual abacus in my mind's eye.
For reference and comparison, one of the other mental math systems is the Trachtenberg system. Soroban is much faster, but Trachtenberg is quite reasonable to teach people of any age.
I've looked into this before. I gave up. It had little utility, even in daily life because humans make mistakes regularly. I have a mathematics degree so it's not like I can't do it but I quote one of my tutors "better to use a calculator than fuck it up and find out a page of working later". So I use a calculator.
Smart. This is kin to a circus trick, a thing that impresses people but in reality has little to no actual value. It could be useful in some settings though, like at a party, interview or impressing an investor or even a potential partner.
I used to learn abacus and had do it for 2 years..
I am not sure if its me but I could've easily done 2 digit calculations in literal seconds... using the abacus model
Then our classes of abacus were shut and the thing is, that now I found myself a slight degradation because with abacus there was an assured confidence but then after abacus I used to blunder tiny things like 6+7=15 and 7*6 and other things.
Maybe my personal experience with abacus was how it ended. I had it for 4 semesters and got 4 medals in abacus for getting full marks but I still believe that it made my common maths, which it meant to improve a little weaker because well now although I don't pull up an abacus in my mind, I still have all the learning of basic things like 6+7=13 and other stuff but for some utter magical reason, learning abacus made me confuse it.
Overall it was a great experience though, seeing my cousins surprised that I was doing 2 digit numbers like 42x 37 calculation in 10 seconds in my mind while playing pass ball at 5th grade, maybe that was one of my peak achievements as I guess I have forgotten abacus completely...
I also remember one of my cousin saying that abacus looks like a music instrument and he used to make a little music out of it. Maybe fun times indeed. I remember it was the same day that I discovered the badlands biome in minecraft, maybe I was in 4th grade. Gold is really common in badlands, I remmeber going into the cave if I am correct.
Edit: also I meant not any hate towards abacus or maybe its just skill issue from my side and I just felt like saying it. I don't know why but for the most part although I still do these mistakes, I used to do it on a much higher frequency after stopping abacus and then covid hit and although I was a strong math student logically, I used to do some mathematical blunders.., for the most part they happen rarely now but still they sometimes do exist when my brain gets into too much auto pilot mode and I usually just prefer to solve calculations in the end because of this in any question or whatever, and maybe only just simplify things at most in intermediate steps so that I do least amount of mistakes possible. I usually don't think about this too much but I used to think that damn I am bad at this and used to remember the abacus past but then I saw some comments on reddit etc. saying that there were whole calculus phd teachers who sometimes did silly mistakes and maybe it was okay... felt really better about myself.
They show an image of it, it's that vertical abacus. They say it's popular in Japan. They have made a digital version of it, used a big keyboard as input, and gamified the practice. They also record how fast they can do calculations and stuff like this.
The point is for the author to understand how they learn (how many things become automatic in his brain and when, mental chunk formation, when performance plateaus). They just use the Japanese abacus as an excuse to do it.
Thank you. I went back and... never would have guessed in a million years they were expandable.
They just look like summary bullets.
Why would anyone write an article where the first paragraphs were collapsed anyways...? But then later paragraphs are expanded, so you think that's where the article starts?
This may actually win the award for worst UX I've seen this year. Because it never gives any indication there's any UX at all. Just, wow.
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:
-----
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
-----
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.
A nice anecdote from Richard Feynman vs a soroban user
https://www.ee.torontomu.ca/~elf/abacus/feynman.html
And HN discussion: https://news.ycombinator.com/item?id=27934887
Nice write up!
I've got a soroban but never got around to learning it. Definitely should pick that up again.
When I was at Uni (electrical engineering) I noticed that the Chinese students would reach for their calculator way less than western students and assumed that was because of the abacus.
Side note: they tried to shape a control theory subject (everyone was getting 100%) by disallowing calculators in tests. It was rough having to do things like long division for the first time in decades. Still everyone got 100% haha.
Author here. Very surprised to see this on HN years after I stopped!
Also, thanks for the UI critique, points taken! The design decision was to hide nitty gritty detail about the background unless the reader was extra interested, in hopes of making an article with gradual / adjustable depth so readers who aren't as interested can get a tl;dr for each section (I still don't know how a nice UI to do this, although LLMs make the idea more in reach now).
I love this idea for how we could have dynamic LoD for articles. I've thought about this a lot over the years and also never landed on a great ux. Maybe llms will help us; it would be great to see these tools shape novel, powerful ux (in the hands of the people).
Thanks for your articles. About your "The surprising benefits of disciplined, deliberate self-logging", I couldn't understand and it seemed cryptic how you're logging? The biologger.md is throwing 404. Could you explain?
Wow, thanks for digging! Looks like I haven't committed that file! It's an incomplete description of the android app that I wrote to output the jsonl in the self-logging piece going through some comparisons of existing options in 2019 and design decisions for the app. In short, it's like myfitnesspal tailored to my use case. 3 years later, the data is still a sprawl, but the logging strategy is stable.
Why the custom computer keyboard? Why not practice on a real soroban? They cost about US$10. You need to practice the finger motions, after all. They're not bad for addition and subtraction. For adding up small numbers, such as at a store checkout, a soroban is still useful. Multiplication, division, don't go there.
With a soroban and a slide rule, you can do most basic engineering problems.
I wanted to track my progress to the highest level of detail possible. The motor motions are somewhat similar, but slightly more complex, than typing on the keyboard. But since I already type fluently I wouldn't be able to get as fresh data, so the soroban was a nice other task.
The main goals were to track learning progress and truly experience what it meant to have a virtual abacus in my mind's eye.
Honored to get a comment from you!
I haven't had to use a soroban in many years, but I did use one, along with a slide rule, in high school physics.
I have used this app for a while: https://play.google.com/store/apps/details?id=br.net.btco.so...
It's really clean and good.
For reference and comparison, one of the other mental math systems is the Trachtenberg system. Soroban is much faster, but Trachtenberg is quite reasonable to teach people of any age.
I've looked into this before. I gave up. It had little utility, even in daily life because humans make mistakes regularly. I have a mathematics degree so it's not like I can't do it but I quote one of my tutors "better to use a calculator than fuck it up and find out a page of working later". So I use a calculator.
Smart. This is kin to a circus trick, a thing that impresses people but in reality has little to no actual value. It could be useful in some settings though, like at a party, interview or impressing an investor or even a potential partner.
I used to learn abacus and had do it for 2 years..
I am not sure if its me but I could've easily done 2 digit calculations in literal seconds... using the abacus model
Then our classes of abacus were shut and the thing is, that now I found myself a slight degradation because with abacus there was an assured confidence but then after abacus I used to blunder tiny things like 6+7=15 and 7*6 and other things.
Maybe my personal experience with abacus was how it ended. I had it for 4 semesters and got 4 medals in abacus for getting full marks but I still believe that it made my common maths, which it meant to improve a little weaker because well now although I don't pull up an abacus in my mind, I still have all the learning of basic things like 6+7=13 and other stuff but for some utter magical reason, learning abacus made me confuse it.
Overall it was a great experience though, seeing my cousins surprised that I was doing 2 digit numbers like 42x 37 calculation in 10 seconds in my mind while playing pass ball at 5th grade, maybe that was one of my peak achievements as I guess I have forgotten abacus completely...
I also remember one of my cousin saying that abacus looks like a music instrument and he used to make a little music out of it. Maybe fun times indeed. I remember it was the same day that I discovered the badlands biome in minecraft, maybe I was in 4th grade. Gold is really common in badlands, I remmeber going into the cave if I am correct.
Edit: also I meant not any hate towards abacus or maybe its just skill issue from my side and I just felt like saying it. I don't know why but for the most part although I still do these mistakes, I used to do it on a much higher frequency after stopping abacus and then covid hit and although I was a strong math student logically, I used to do some mathematical blunders.., for the most part they happen rarely now but still they sometimes do exist when my brain gets into too much auto pilot mode and I usually just prefer to solve calculations in the end because of this in any question or whatever, and maybe only just simplify things at most in intermediate steps so that I do least amount of mistakes possible. I usually don't think about this too much but I used to think that damn I am bad at this and used to remember the abacus past but then I saw some comments on reddit etc. saying that there were whole calculus phd teachers who sometimes did silly mistakes and maybe it was okay... felt really better about myself.
Author never explains what soroban is or how it works, so I really have no idea what's going on here.
They show an image of it, it's that vertical abacus. They say it's popular in Japan. They have made a digital version of it, used a big keyboard as input, and gamified the practice. They also record how fast they can do calculations and stuff like this.
The point is for the author to understand how they learn (how many things become automatic in his brain and when, mental chunk formation, when performance plateaus). They just use the Japanese abacus as an excuse to do it.
You didn't click all the details? The first section describes it in depth.
Thank you! I didn’t realize those were expandable until I read your comment.
The black triangle bullets are expandable, folks, and worth expanding.
Thank you. I went back and... never would have guessed in a million years they were expandable.
They just look like summary bullets.
Why would anyone write an article where the first paragraphs were collapsed anyways...? But then later paragraphs are expanded, so you think that's where the article starts?
This may actually win the award for worst UX I've seen this year. Because it never gives any indication there's any UX at all. Just, wow.
Aha, I thought they were just bullet points. Terrible UI!
thanks, I thought I was just dumb
Click on the bullet points. They expand.
Maybe just happy?