3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588…You can tell from the first three or four digits that this whole bunch of numbers represents a simple idea, the ratio of a circle to its diameter, π. Now, if I say that the person who can memorize the most number of the decimals of pi can win a million dollar prize, what strategy do you think is the most effective, and how many decimals do you think are enough to win the prize?

One strategy that may come to your mind is creating little chunks of decimals of pi and memorize chunk by chunk. For example, the first 20 digits can be chunked into ‘31415,’ ‘92653,’ ‘58979,’ and‘32384.’ The last one or two digits of the previous chunk may cue you about the first one or two digits of the latter group. However, after you memorize a considerable number of decimals, you will find it difficult to continue because the digits cues start to repeat and you will experience too much retroactive interference, which describes the phenomenon that things memorized later may negatively affect your ability to recall something memorized earlier. A similar thing happens when you are trying to remember two people’s phone number. After you memorize the second phone number, the first one will appear to be a bit vague in your memory. You can choose to enlarge the group size from 5 digits to 10 digits to reduce the cue repetition, thus the retroactive interference can be reduced as you are using more digits as cues. However, you may still find it hard to continue after you reach a certain part when all the digits and cues entangle and you cannot recall them in a correct sequence, which is the key of memorizing pi. Due to the difficulties you find, you may come up with a reasonable estimation and wisely give up because it is kind of a waste of time.

If your estimation is about 1000 decimals, you are far from the prize. To win the million-dollar prize, you have to defeat Chao Lu, a Guinness Book Record holder, who perfectly recalled 67890 decimals of pi. It’s too crazy to be true, right? Memory contributing to memorize pi is long-term memory, which basically stores everything that you can recall from your birth to about five minutes ago. Long-term memory has extremely large capacity of storage, but you cannot retrieve things back from long-term memory as quickly as you want. One problem that can happen while recalling the decimals of pi from long-term memory is that the decimals might be stored in your memory, but you cannot actively retrieve them. This is similar to the situation when you cannot tell the name of someone you see, but you are certain that you know the name of that person. This kind of tip-of-tongue situation can be deadly while you are reciting the decimals of pi because you cannot say that ‘I know I know the decimals, but I just cannot recall them now.’

The way that long-term memory works is that linkages are formed between items in long-term memory. When an item in long-term memory is actively retrieved, things connected to that item are also to some degree activated. Whether you recall the things connected to that particular item depends on the degree of activation. You may miss something you want to recall due to its low activation level, but you may also report something you don’t want to recall due to its high activation level. It is reasonable to suspect that Chao’s long-term memory is just exceptional, so that he can always activate the correct item in his long-term memory and recall it despite the degree of activation. However, Chao’s long-term memory is nothing different from yours or other normal people’s memory. To avoid the tip-of-tongue situation, Chao and other people who have exceptional memory for certain areas are able to adopt the help of long-term-working memory (LTWM). People who use LTWM have acquired memory skills, which allow them to encode information in long-term-memory in a retrievable form. This means that with the help of certain memory skills, they are 100 percent sure that the information which they stored into long-term-memory can be retrieved in a correct pattern immediately in all situation.

To get access to details of Chao’s acquired memory skills, Yi Hu and Anders Ericsson conducted a study on how Chao’s strategy for memorizing an extremely long list of numbers works. They specifically conducted experiments to examine the validity of Chao’s self reported story mnemonic strategy. The strategy includes coming up with different images for each two digits number from 00 to 99. With the one hundred images, Chao is able to memorize digits of pi as a story connected by multiple images. Each image serves as a cue for the next image in the story. By memorizing multiple different long stories, Chao is able to reach his astounding record of 67890 decimals of pi.

The first experiment examined the reliability of Chao’s connection between two-digit numbers and the certain images, as well as the reliability of the connection between two images as cue for the latter image. Chao was asked to memorize two 100-digit lists in the experiment, and was asked to recall all of them during the same test session. He came up with one long story for each list. According to his report, the images he came up with for the each two digits in the lists were highly consistent with the number. The pairing of the two-digit number and the image was strong. However, when two two-digit numbers repeatedly appeared consecutively in the lists, he came up with different connection between the two images each time. For example, when he memorized 1546 in the fist occurrence, he came up with the sentence ‘Parrot (15) is flying to the dead deer (46)’, but he came up with ‘parrot (15) is looking for dead deer (46)’ in the second occurrence. This indicated that the connection between two images was the key for Chao to use the former image as a cue for the latter image. The way he connected pictures to form meaningful stories follows one of the principles to form better long-term memory: people memorize better when they process the information in a deeper level. For example, it is a lot easier for you to study words from a foreign language when you know the meaning rather than just reciting based on the combination of letters. Knowing the meaning indicates a deeper level of processing than knowing the sequence of the letters. In this case, when Chao chose to memorize using a meaningful story, he engaged in a deeper level of processing than directly memorizing the sequence of the digits.

The second lab experiment was designed to further test how Chao’s story mnemonic works and how former images cue latter images. After recording Chao’s study time and recall time for a 100-digit list, the researchers found out that his study time for the first two digits was the shortest within the group of numbers which he used to form a story. The study time increased as he reached the end of the group of numbers. This phenomenon was reversed for the recall time. The first two digits, in this case, took longer to be recalled. One explanation is that while studying, Chao spent more time studying the last digits because he had to rehearse the preceding images to solidify the cues connecting all the images. When he was recalling the digits, it was most difficult to recall the first digits because they appeared at the beginning of the story and there weren’t enough cues.

After I tell you how Chao memorized the crazy long list of digits, you may find it reasonable for him to break the Guinness Book Record. It is not about his super brainpower, but his strategy to memorize information in an easily retrievable way. We are normally not required to memorize such long list of numbers in our life, but it is still useful for people to come up with methods to connect things with unique traces and reduce retroactive interference. It is all about strategies. For items that don’t have traces connecting each other, it is probably a good idea to come up with objects related to each item and form traces based on the objects. It might be a lot easier to form connections between objects you come up with. In order to distinguish similar concepts in your memory, you may connect them to different related ideas, so that you can use the related concepts to distinguish the original ones. This is also a take home point from Chao’s strategy in which he use different connections between two of the same images in different situations to distinguish different cues. It’s always useful for you to come up with memory strategies to memorize all those ‘pi’s in different fields.

To read the original paper, click here

To read a related blog about memory strategy, click here

Reference:

Hu, Y., & Ericsson, K.A. (2012).  Memorization and recall of very long lists accounted for within the Long-Term Working Memory framework. Cognitive Psychology, 64, 235-266