Calculating the Size of the Working Memory of the Human Brain

We’ve seen before that the maximum speed the of human brain is about 60 bits per second, which of course is super slow compared an electronic calculator. However it’s not the only challenge that the human brain faces when performing difficult mental math!

Imagine you were asked to to find out what the most popular car colour is in your area, by watching the traffic passing on a particular road for half an hour.

Red, black, white, white, blue, black, silver, red, white, …

You could simply set up a tally, and at the end check which car was seen the most. It would be a very easy, almost mindless task.

But now imagine that it was raining and you couldn’t write anything – your only tools were your eyes and brain. Now how would you do this? Suddenly it becomes much, much harder!

Without being able to store anything on the paper, you are restricted to using the working memory of your own brain to store anything you would write on the paper – and that is very limited indeed.

Working Memory and Mental Math

This has profound implications for mental math, because we can only handle numbers using methods that “fit” inside our working memory. (With practice) we may be able to solve 4587 ÷ 11 by simply removing multiples of 11 from 4587:

4587 – 4400 = 187 … and 187 – 110 = 77 … so the answer is 417

But it’s very difficult to solve 1744982049 ÷ 54903 by subtracting multiples of 54903 because we quickly end up trying to store more numbers in our mind than we can handle. (Luckily there is a much easier method for performing calculations such as these).

So if our limited working memory (analogous to the RAM of an electronic computer) is so important for mental calculation – how much of it do we have?

Baddeley’s Model

The widely-accepted model for the human working memory was proposed by Psychologists Baddeley and Hitch (1974) and states that it has two main components:

• Phonological loop: a short loop of sound that can be continually repeated and modified
• Visuospatial Sketchpad: a basic color image (or video)

Size of the Phonological Loop (PL)

According to research by Psychologist Miller in 1956, we can remember between 5-9 “chunks” of information when stored in our inner monologue.

Simpler chunks (such a binary digits) may be slightly easier than complex chunks (such as words) but they fall regardless in the same 5-9 range. And certainly when the chunks are numbers 0-9 it’s been shown experimentally to follow this pattern, whether they are spoken aloud to us or whether we read them using our inner monologue.

It’s easy to test this for yourself – for each of the following, carefully read the number aloud, and then write the number down without looking.

Now, we would expect a higher PL capacity to improve mental calculation ability. However in workshops I’ve given where I’ve performed this experiment, even the top human calculators are unable to recall more than 8-9 digits spoken in their native language. How many did you get in the experiment above?

This illustrates that the limit is fairly uniform among people – or possibly that top human calculators rely more on their visuospatial sketchpad than their phonological loop.

Size of the Visuospatial Sketchpad (VSS)

One of the most impressive displays of mental calculation ability is flash anzan – where a sequence of numbers is flashed on a screen, and the task is to add these up. This calculation category is dominated by students of the soroban abacus, who perform this entirely visually (and can even hold a conversation at the same time!)

The human calculator above is soroban master Naofumi Ogasawara breaking a flash anzan world record at the Mental Calculation World Cup in 2012. The most impressive thing here is that he is working with 5-digit numbers! Since the answer will be a 6-digit number this suggests that he is able to store 6-digit numbers in his VSS comfortably enough to also perform mathematical operations on them.

Naofumi is not the only person able to handle such large numbers in this way. For example Jeonghee Lee, who won the flash anzan event at Memoriad in 2016, and is the current world record holder for addition, has also demonstrated equivalent ability as Naofumi.

Another simpler way to measure the the size of your visuospatial sketchpad is to look at a string of numbers (but without saying the numbers aloud in your mind) and then write it down a moment later.

You must not use the phonological loop! You can help avoid this by reciting an unrelated phrase aloud, or by listening to music with clear lyrics in your native language.

If you want to try this yourself, put some headphones on now before revealing the numbers below (as you only get one chance to try).

What was your score? For me level 6 is difficult.

Clinical measurement of the size of the VSS is typically tested experimentally using the Visual Pattern Span Test. I couldn’t find a good online test for this – so if you find one please contact me to let me know! A high score seems to be about 15 squares, although again there are very few results online for adults.

15 squares would be equivalent to 4-5 decimal digits (since 15 * log 2 = 4.52) which is a little lower than our figures of 5-6 digits from the previous paragraphs. This perhaps shows that with practice, we can learn to use our VSS more effectively when dealing with numbers.

Combining the Phonological Loop and Visuospatial Sketchpad

A natural question to wonder now is whether we can utilize these two types of working memory simultaneously, or whether we have a total limit that can be assigned to either. It turns out it is possible to use them simultaneously near to full capacity, although it requires greater concentration.

In fact this is used by some participants in speed memory events, such as memorizing a pack of playing cards. After using their standard mind palace system for the majority of the cards, they can quickly store the remaining cards between their phonological loop and visuospatial sketchpad, and therefore finish the memorization stage earlier for a higher score.

You can try this for yourself by memorizing the following 10 digits – more than can fit in either half of your working memory! Simply look at the image of the last 4 digits to put them in your visuospatial sketchpad, read the first 6 digits aloud to put them in your phonological loop, and finally glance again at the last 4 digits to ensure that they are still clear in your VSS.

Then immediately write the full number down on paper. How was it?