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#1 18 February, 2016 - 16:47
Joined: 3 years 3 months ago


I have been started playing with anzan recently in order to try to improve my numeric processing time at bit with practice.

I have quickly found that subvocalizing puts a severe limit on my ability to process. If I visualize rather than mentally speak the results basic addition time improves instantly and significantly (although it is going to take me some practice to stop saying the numbers in my head). Oddly I stopped subvocalizing the written word at an early age but apparently I have never done so with numbers.

On to the question... With speed memorization do you make an explicit effort not to vocalize when you are memorizing OR is this the verbal component necessary to creating the chain and limits the speed of memorization?


19 February, 2016 - 01:05
Joined: 4 years 9 months ago

I use subvocalizing but I don't even notice it. I might try some mental math without subvocalizing

19 February, 2016 - 04:00
Joined: 2 years 6 months ago

One of the first books I read on memory techniques suggested that sounds, smells, and emotions be incorporated with visual images. When I memorize cards or numbers I make a conscious effort to incorporate sounds and subvocalization. Right now I belief that subvocalization helps me more than is a detriment to faster memorization.

I am only speaking from experience in memorizing cards/numbers and not mental math calculations as you are describing. I have not used the major system but all those images are associated with letters to create words.I am curious to know if people who have become very good with those type of word based systems use subvocalization or decided at some point that only creating a visual image was necessary.

19 February, 2016 - 04:26
Joined: 4 years 11 months ago

What the memory book was intending to teach you was that sounds which are relevant to the imagery itself, such as the popping of a balloon, the giggling of a baby, or the harrowing wails and bloody gurgles and vomiting of a man being quartered by horses, will embed the imagery more deeply into memory. If you sneezed while memorizing, that would not count.

Your post is intriguing Robert. I believe you are honest, but unfortunately I am not able to believe you are correct. I remember an early experiment measuring invisible muscular movements in the hands of the deaf who were showed words/imagery. That isn't terribly strong evidence to support my point, but is interesting nonetheless. I personally do not think that a literate person can rid themselves of subvocalization, so it is very curious that you perceive yourself to have done this. Yet it is not enough to sway me from my position, though it does some work in that direction.

Anyone else agree? Anyone think that I'm so skeptical that it counts as "mean"?

19 February, 2016 - 16:04
Joined: 3 years 3 months ago

My reading speed (400-600 wpm - fiction) is far more than double my ability to speak those words (150 would sound like an auctioneer). I think most fairly literate people can read significantly faster than they can speak. This is not in any way abnormal so your skepticism is duly noted but simple experiment should make it clear to you that it is true.

My ability to add however is limited to the speed at which I can say the numbers unless I consciously make the effort to visualize the result rather than say it (subvocalize) which I do habitually. I can not add much more than a digit per second sustained if I sub-vocalize. Without practice by concentrating on the image result rather than the spoken word my result were immediately digit/.8 seconds and although retention of intermediate terms was 0, calculation of the result was much less stressful. I suspect with further practice getting down to .5 sec/digit shouldn't be too tough. I seem to brain fart on the 9's which isn't surprising to me. Multi-digit manipulation may be a tougher nut to crack.

19 February, 2016 - 16:36
Joined: 2 years 6 months ago

Robert I have a question about how you perform these mental additions. I have no experience with this type of numeric processing and I am very curious about this type of mental math.

Have you seen the TV show Superhuman on FOX? One of the competitors is named Yusnier Viena and he does flash math. On the TV show he performs 3 exercises of mental addition. A set of ten 2-digit numbers were flashed on the screen and he had to add them all up. In each round the time of each flash decreased to the final round where it was flashed on the screen for 100 milliseconds. My question for you is this format similar/identical to how you perform numeric additions? You did mention that you can do a digjit/.8 seconds so I’m assuming that is how long the number flashes for? On the TV show he added 10 digits. What is the maximum number of digits you add?

In regards to sub vocalization- If you watch the TV show Yusnier stares at the screen while the numbers are flashing. Once they have stopped flashing he looks down in concentration and you can see his lips moving slightly. So he is clearly doing subvocalization while adding these numbers. My question for you is do you perform a similar type of subvocalization when you are adding the numbers after you have stopped looking at the last digit? Or do you add the numbers together while looking at them so you once the last number if flashed you immediately know the answer? Thanks

19 February, 2016 - 21:05
Joined: 3 years 3 months ago

I add them while looking at them... I have no memory of the sequence as the digits whiz by... although occasionally when I stumble I try to grab subtotals but without much success. I have not internalized the major system (or any other for that matter) so holding onto strings of digits is extremely difficult for me.... (that would be another project.)

Give it a try to see what I mean...
euro anzan lets you control the timings to the 100th of a second which is nice (pc)

Android has an app as well.

The memoriad competition simulator has a flash anzan version but you can't control the speed (.5 seconds) so it's not terribly useful for me (I'm too slow still). Both flash anzan and spoken word.

My wife came into my office earlier and asked me what the hell was going on. I had my headset on and apparently was making some very odd sounds attempting to add without subvocalizing. It's surprisingly tough.

The "normal" flash anzan players visualize an abacus and manipulate it in their heads. I am attempting to visualize numbers rather than an abacus and it is tough but doable. Whether I can become proficient is another question entirely. The japanese children who have learned mental abacus techniques are stunningly fast. Far faster than spoken word is possible. Sadly, old guys generally don't learn new tricks with nearly the same speed or success. Hopefully, I can improve significantly on my current state and leverage this as part of improving my core numeracy, mental calculation and studying math. I should really learn the major system soon. I've started a few times now but never nailed it down and made it permanent.

try googling "youtube flash anzan" for obscene examples.

When you see the flash anzan players talking to themselves while entering the digits they are interpreting their mental picture of the abacus that they have manipulated into numbers. They have not remembered the sequence but are transcribing the picture.

I've been playing at the 10 repetition level as it makes it easier to start again when I fail. 60 seconds would probably be better if I could sustain it as 10 single digits doesn't get me into the 100's. Once I get a little less crushed by single digits I will probably start 2 digit numbers.

Flash anzan competitors are doing .5 seconds and many (8, 9, 10) digit numbers.... 10,000 hours of soroban practice and talent. I have neither of these going for me but improving my processing time in mental calculation seems a worthwhile endeavor even if my success will be limited.

20 February, 2016 - 07:37
Joined: 4 years 11 months ago

A quick response Robert. Firstly as far as mental addition goes, maybe I should hand it to you on this one. May not mean much to you, but it's important to me. :) Firstly I don't have experience with your brand of math, but the experience of my own mental calculations for addition, subtraction, multiplication and division is in terms of imagery typically in squires divided and colored like "bar graphs," where each 'bar' has little marks on the side like a ruler when zoomed in on, and these can be zoomed in on indefinitely to show further small marks in groups of 10, but where the fifth is slightly larger. So in terms of addition, this is basically like stacking transparent rulers on one another and counting the number of marks from the 5 or the 10 where the rulers intersect, which is quick because you don't actually have to 'count' within a group of 5. " l l l l l " it is quite easy to pick out the third or fourth there without counting to it for example. Division is the same, but you just turn one bar horizontally and divide it up with the right number of little squares, easy to 'count' to when you zoom past the tens, easy to count where the bar stops being shaded since they are divided in 5's and 10's, then with each zoom, you 'count' to arrive at that digit place's value, and then you zoom into the edge of the shading on the last block, which is only partially shaded, and you continue to zoom in closer and closer to find the decimal values, again not difficult because of how easy it is to determine numbers within 5 just by looking at them. I'm probably lucky to have started conceptualizing this way early on while playing with blocks or something like that because it's pretty efficient. Anyway, I don't think that process requires subvocalization since it is entirely visual. So even in different form, if you totally "get" how that experience is like yours, then I understand you better now. I never thought of it that way, in terms of math which is an expression of language. A good realization or at least change of heart, so thanks for this.

But what process is the "reading" counterpart. I can't even comprehend fluently reading a language with all its complexity with a process like this. I only have to work with ten little tick marks when it comes to any sort of calculation, but words? Maybe in theory it could be done, but no one does it.

WPM means absolutely nothing, so I'll bet we're on different pages when it comes to defining "subvocalization." I only think that the elimination of subvocalization is impossible. Everyone truncates subvocalization to read, and with training I imagine you could take this very far. That clause, "I imagine you could take this very far," is pretty simple. It's predictable too, given the context. So I think I'm skipping some words there. And phrases like "all of the" also won't take much (or maybe zero) subvocalization with enough practice. You can skip syllables, entire words, maybe sentences if they're short enough, but with no requirement of muscular movement in the throat and tongue, or no representation of the word in terms of audio loop, what is the factor that limits your reading speed so much, in your opinion? This is how the words were learned, so to eliminate subvocalization I assume all words would have to be relearned in some new way that is foreign to me, and learned them all well enough to replace this lifelong understanding. What a task. Anyway, I guess I'm splitting hairs. If you can't detect the subvocalization then I suppose for all practical purposes excluding fMRI research, you can do it. I'm comfortable with standing on small ground. And since you don't believe it is a limiting factor on reading speed, that is an important thing for us to know. But again I'm curious, what do you think are the best candidates as limiting factors?

20 February, 2016 - 10:30
Joined: 3 years 3 months ago

Clarifiying "subvocalization" is probably a good place to start... We can probably discuss this better as a range of effects. Am I thinking in the language that I have learned to read? Yes. I would describe my experience of reading fiction as more like listening than speaking. It is different than when I am typing for example and the words are more closely linked to my speaking. I tend to imagine the voices and visualize the characters speaking dialog rather than my own voice reading words. I think the MRI would show two fairly distinct patterns between my consumption of the written word/spoken and my authoring the written word/spoken. Is there unconscious electrical activity in the pathways that link to speech. Most likely, but I do not notice myself attempting to make monkey noises when I am listening to others speak or engrossed in fiction and I am not limited by the speed of my tongue or throat muscles.

The addition example that I started this thread with results in monkey noises. I am not only imagining saying the numbers but my ability to add is limited by the speed that I can speak the numbers.

Your hashmark example for calculating is a simpler version of the abacus/soroban method using visualization to collect totals and aid numeric manipulation without language.

I may have to (may not be able to) learn a similar system. My initial, trivial observation, is that if I focus on the image of the additive result and attempt to read the numbers rather than add/speak the numbers then my processing speed is significantly faster.

This is also mixed in (muddied) with familiarity to the exercise (practice). I worked down to 0.4 digits per seconds last night but couldn't get much past 4 numbers ( I stumble on similar addition points each time... mostly 9's).

Single digits 0-9 addition appears to be something that is not overwhelming to visualize rather than say. It may entirely fall apart at 3,4,5 digits ... I am unsure. I suspect 2 digits is something I may be able to manage. The approach of using soroban is well proven when started in childhood. I haven't found anecdotal evidence of anyone learning mental soroban in adulthood but hopefully someone will notice this thread if so. Our initial number systems were all III II III and probably for a very good reason. The challenge with these symbols is that we aren't very good with visually interpreting the difference between IIIIII and IIIIIII while II and III are trivial for us to recognize. One, two, three, many. Differentiating between 6 and 7 is a pretty big stretch for most people. This may be why hashmarks, using complements adding/subtracting, and the soroban work so well.

It could also be a perfectly good explanation why, if after initial improvement through practice, my improvements will hit a wall using this approach while abacus masters do crazy things with multi-digit numbers in the .4/.5 second time frame. On the other hand, I would be happy to see a 100% improvement in basic addition/subtraction processing time in my mental calculations even if others are 1000% percent faster (1000% percent would be great too, but despite owning a soroban and having spent a few dozens of hours practicing I suspect I am not likely to become a soroban master). In the mean time, I'm going to give it the old fashioned 6-8 weeks of daily practice and see what happens. If it can get my 3x3 mental multiplication fast enough that I quit stalling on subtotals I would consider the experiment a practical success.

There is a second layer to this question, left undiscussed. In competitions, such as the memoriad, are competitors retaining multi digit numbers being flashed at .5 seconds and how long are they able to retain and manipulate them for? ... and can this level of skill be acquired as an adult?

The ability to quickly sustain 10 relatively large subtotals in short term memory would be extremely beneficial to all sorts of calculation... I have been looking forward to playing with "mental algebra", "mental calculus" and thinking wouldn't that be nice...

20 February, 2016 - 22:39
r30's picture
Joined: 3 years 11 months ago

Well, i've pondered over the same thing (subvocalization or not?), and concluded that what's essential in the end, is for the brain to have a strong stimuli which it can concentrate on. Vocalization is strong stimuli, also touch. But from my experience visualization is not. Loud voice forces you to close your ears, painful stabbing makes you pull your hand away, awful smell automates you into closing your nose... But whatever how brute video without sound doesn't make you look away. I've tried speedreading and visualizing math completely wihtout subvocalization, but it hasn't worked for me. Guess it needs stronger stimuli than pure visualization to pull out the meanings of the words from the depths of the mind. However it is possible to reduce the subvocalization to minimal (like only uttering like "mh, mh,,, mh" to force your concentration on specific task). Or chinese use their fingers with the abacus:
the touch with or without the abacus is strong stimuli (I've seen videos where the mental athletes still move their fingers when calculating).

21 February, 2016 - 10:04
Joined: 2 years 3 months ago

Fantastic video, thanks! Calculation with an imaginative abacus is really impressive.

21 February, 2016 - 10:31
r30's picture
Joined: 3 years 11 months ago

Then you mental athletes might also be interested in what we Estonians call "Pranglimine"
Most of students practice it since the 1st grade for the next 9 years, and they get quite pro. I also own my fast calculation skills to that web program.

21 February, 2016 - 16:49
Joined: 3 years 3 months ago

Chisenbop (korean finger counting system) is another method for calculation that takes the load off of verbal skills in a manner similar to soroban or loci's hash marks. I suppose I will have to give one of these methods 16 or 20 weeks consistent effort to see if I can get one to stick but as I said so far my limited practice with an adult has me only able to do rather poor and slow addition with a physical soroban. From the perspective of using the hindu-arabic numbers the first obvious improvement in mental calculation beyond raw familiarity with addition and subtraction of 1,2,3,4,5,6,7,8,9,0 is almost certainly equally fast recognition of complements of 10. Both Hadley and Benjamin emphasize this in their mental calculation textbooks. This has the remarkable advantage of being able to constrain addition to 5 hashmarks and a carry which is a load that fits perfectly into Loci's mental imagery and is also a primary reason that a soroban has 5 counting beads rather than 9, 4, or 10 (depending on how you might organize your thinking).

Round number one for me is brute force - learn +/- 0,1,2,3,4,5,6,7,8,9 single digits at a rate of .5 seconds
- stretch to 2,3,4,5,6 at whatever rate happens.

Round number two is likely learn complements to the same extent.
- stretch...

Round 3 - Combine 1&2 at higher rates of speed and/or complexity.

Round 4 - learn a visual counting techique??? I'm unsure if I want to go this route.

Round 5 - From a memory perspective it would be amazing to be able to concurrently remember the intermediate numbers. Is anyone here able to both calculate and create a peg list/journey at speed?

I'm not terribly interested in being a one trick pony but I'd like to exercise the 80/20 rule here and get what improvements in processing speed I can without commiting to a purely visual system.

The reason for this is that I would like to take whatever "numeracy" / improvement in processing speed that results from this and leverage + and + to * and /, pow, roots, logs, algebra and calculus.
It "seems" to me that effort in the understanding of numbers "should" pay off in later mental flexibility.

Mathematicians in the time of Euler and the Bournoulis had developed their numeracy to a high level without the aid of soroban type methods and the resulting Mathematics seemed to have been quite good. The oriental counting techniques seem to be faster and more accurate but it's not as clear to me that they result in a similar depth of mental model of mathematics.... Although I could be entirely wrong (I often am) and if Euler had learned a visual/physically based counting technique he may have been even more amazing.

23 February, 2016 - 04:23
Joined: 3 years 3 months ago

... just a note so I can read it later...

The variability in mental processing speed.... On waking vs fully caffienated seems to wash out any kind of "learning" estimate that one might hope to measure. It appears I am as dumb as a post first thing in the morning even though I don't recognize it consciously. You would need a large sample size of monkeys, double blind testing, and some darn good stats just to show correlation let alone causality. Finding patterns in noise is much too easy.

Anecdotally, it is less stressful for me to get the wrong answers at higher speeds both in anzan practice and in attempting to mentally calculate 3 digit multiplication after 4 or 5 days. Actually getting the Right answer would be a lot easier to measure as the difference between reduced anxiety with being wrong and improved processing are easily confused. Sadly, I am not getting the Right answer. I am instead making my incorrect calculations more quickly. ;) .... another bit of wisdom from she who must be obeyed. "You can't fix stupid".

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