Using the Coordinate System to Memorize Pi
Just as it is impossible to calculate all the digits of pi, so it is impossible to memorize them. Fractions such as 22/7 or 355/113 can provide useful working approximations – but that is all they can ever be. Using such fractions is not a recognized way of remembering pi. If you really want to memorize pi then try the coordinate system for up to 5,200 digits.
The coordinate system for memorizing pi uses a grid system to encode four digit groups using words based on the Major system using consonant sounds, and is capable (unmodified) of storing 2,600 digits.
For this advanced technique you need to be familiar with the Link System and the Major System. There are some variations on this method – lists or grids. We will use the grid approach here. You can easily set this up with a spreadsheet. Picture a grid with letters of the alphabet along one side, and the digits 0-9 along the other. That’s 260 cells. We only include the digits after the decimal point.
You do need to be clear about how many digits you plan to remember, as that influences the basic grid design. If you are aiming for several thousand digits, then you will need to store 10 digits in each cell. For simplicity here, each cell will contain 4 digits of pi.
The first 4 digits of pi will be associated with cell A0.
First, encode the cell ID using A (the row identifier) and ‘saw’ (0 from the Major system). Then, again using the Major system, encode the digits 1415 for example, TuRTLe. Now make the mental image link between ‘saw’ and ‘turtle’ (the Link system) and record the words ‘saw-turtle’ in cell A0. So on and so forth.
This basic grid of 10 x 26 x 4 digits will accommodate 1,040 digits – and don’t forget the first digit, 3, which we left out of the grid.
Pros and Cons of the Coordinate System
The main advantage of the Coordinate system for memorizing pi is that the series of digits can be picked up from anywhere within the remembered series. Also, it is capable of satisfying the needs of most people with its capacity for 2,600 digits, or 5,200 after minor modification. Other modifications can take it further.
However, on the negative side it does require two levels of decoding – the mental map of the coordinate grid and the digit words themselves via the Major system.
How to Beat the World Record for Memorizing Pi
To beat the official world record you would have to remember more than 67,890 digits. This is quite a challenging task. It might be accomplished by visualizing a building with the rooms on each floor being a grid (as described above). You would have to devise a grid for each floor with a floor number identifier on the words. 10 floors would give you 26,000 digits, but to take the official record your elevator would have to take you up to the 27th floor (ground floor = 0).
How to use a Piem to Memorize Pi
The official world record holder for memorizing the digits of pi is Chao Lu, with 67,890 digits. There are higher but unverified claims. How do they do it? Several methods have been devised including using a Piem (a special poem written to encode the digits). However, for a piem to encode that many digits it would have to be 20 times as as long as ‘The Rime of the Ancient Mariner’ (Samuel Taylor Coleridge)!
If you have more modest ambitions, we will explain below how to create a piem to memorize pi. The number of digits to be memorized is then limited only by your artistic ability!
Piems are based on the use of Pilish. This is not really a language (as some others have described it), it is more a style of writing in which each digit of pi is represented only by the number of letters in the word. In this respect it is probably the easiest memory technique to use offering almost complete freedom with your written language, provided it is not based on pictograms – for which other techniques can be used.
For example, this piem written by Michael Shapiro encodes 30 digits:
Now I will a rhyme construct
By chosen words the young instruct.
Cunningly devised endeavor,
Con it and remember ever.
Widths of circle here you see.
Sketched out in strange obscurity.
3.141 592 653 589 793 238 462 643 383 279
Practical Issues of Memorizing Pi with Piems
The Importance of Truncation. When planning to memorize pi, it is a good idea to choose the cut-off point carefully. Truncation allows the piem to be extended in the future (to enable the recall of more digits of pi) without having encoded a rounded digit in the original and therefore needing a change of final word. Precision is preserved.
Structure, Meter and Style. The key aspect here is that unless you plan on unveiling it to the world, or even publishing it (as Mike Keith did with Cadaeic Cadenza encoding the first 3,834 digits of pi), then it really doesn’t matter how elegant it is, or whether it meets any of the regular criteria of good poetry. It only has to serve the purpose of helping you to recall the digits of pi.
The piem can be bawdy, serious, themed on nature, a journey, a lover, space or the sea. In fact, if you can associate imagery with the piem then that will help your memory too.
Of course it is fun to make a good job of it and have something that you would be happy to recite – at least amongst your friends, or in the shower.
Learn to Memorize Pi using the Major System
It is impossible to remember all the digits of pi because it is impossible to calculate them in the first place. By 2013, pi had been calculated to more than 13.3 trillion decimal places (~10^13) and the calculation continues. For scientific purposes, it is rarely necessary to work with more than 40 digits but the memory masters can remember many more.
Here, we are going to consider the Major System for memorizing pi. This powerful memory technique was created by Stanislaus Mink von Wennsshein in the seventeenth century and is widely used.
The Major system is based on a phonetic code of 10 items – consonants – which have to be learned. These represent the digits 0-9, as follows:
0 – S z c
1 – T d
2 – N
3 – M
4 – R
5 – L
6 – Sh ch j
7 – K g
8 – F v ph
9 – B p
The capitalized letters are used to remember the name ‘Stan Marloshkevip’ (vowels have been added). This name acts as a mnemonic for the Major coding system, to help deciphering. Note that the name contains the phonetic consonants in order. Note that there are a few sounds that do not appear, such as ‘oo’ (we only need to represent 10 digits) – these sounds are used as fillers, as are vowels. There are several other ways of memorizing this list, including one based on images. Settle on one method an practice it.
Once you have learned this, then vowels are added to create words. For example, TURTLE, when decoded is equivalent to 1415 (T*RTL* ) ignoring vowels *. There is no real limit to the words that can be created (other than the language itself). Start with simple words using one sound, such as law, fort. Then move on to more complex words.
These words are then used to create a memorable story, or the stops on a travel trip. In a story, it is best to avoid the use of the same word twice, unless for a genuine reason. For example, the string 1415 occurs twice in the first 20,000 digits of pi, 4567 occurs three times, and shorter strings are more frequent. Some users of the system use a list of maybe 100 ‘peg’ words, such as cat (71) and tar (14).
There are many examples of ready-made stories. If you want to write your own then you only need to write it once.
A Generic Method
The power of this method is transferrable to memorizing any string of numbers, from phone numbers to other irrational numbers such as e (Euler’s Number) and √2, if you really want to take on a challenge. A neat trick is to memorize the product of pi * √2 to n digits. Then you can claim that you can multiply the two numbers in your head. Of course, you know the answer already!
The unofficial record holder for memorizing pi is Akira Haraguchi, of Japan, who claimed a record of 100,000 digits in 2006.
How to Memorize Pi using the Link System
Pi is the most widely recognized of irrational numbers. An irrational number is a real number which cannot be expressed as the ratio of two integers. Many people would say that anyone who tries to memorize an irrational number is probably suffering from a degree of irrationality themselves! Of course, it is impossible to memorize such a number as the string of digits is infinite in length and non-repeating.
However, many people do take on the challenge of memorizing pi and there are several quite different techniques to assist memorizing pi – or at least several thousand digits. The memory routine we will discuss here is known as the Link method.
Method – Build a Dictionary
- 1. The first step is to set up your ‘phonetic’ dictionary, so start by assigning each digit of pi a word which holds its corresponding sound. For example, 1 = bun, 2 = shoe, 3 = tree, four = door.
- 2. Next, form words by grouping together these sounds. The words created will suit best if they are actions or objects (verbs or nouns). There are some variations to the method here, as it can otherwise become cumbersome. To add variety, you can have several words for each digit and use a little artistic license. For example:
0 = hero, Nero, bought, caught
1 = fun, run, sun, gun
2 = shoe, rue, blue, glue
3 = tree, free, glee, see, fee
4 = door, floor, more, for
5 = live, jive, Clive, knives
6 = tricks, licks, sticks, picks
7 = leaven, heaven, even seven
8 = late, fate, bate, hate, gate
9 = fine, wine, line, shine
Of course, the numbers themselves can also be used.
Write Your Story
This is the fun part – build a story by linking the words together. Generally, the most effective approach is to create a sequence of events. Poetry too can be used – nonsense poetry tends to be particularly memorable.
For example a piece of prose for 3.1415 926 5358 979 would be:
Free sun is for fun – five fine glue sticks Clive. Free Clive late, shine heaven shine!
Of course, no self-respecting author would claim that as real prose, but it only needs to serve to memorize pi, and not to entertain a reader. You only have to make it work for yourself.
This method has the disadvantage of all association techniques – when reciting the digits of pi it is necessary to carry out real time decoding. It can be quite fun though.
Composite Methods to Memorize Pi
Composite methods can also be used to memorize the digits of pi, so that, say, the first block of a hundred digits uses a story, the next block uses a piem and so on. Then the blocks can repeat – obviously with different stories, as we all know pi does not have repeating patterns of digits.
How to Memorize Pi using Word and Sound Substitutions
It is said that there are two types of people who memorize pi:
- Scientists, who only need to remember a few digits at most for use when discussing science topics (for any more digits they use a computer and rarely need more than 40).
- Science or math fans who see it as a challenge to remember as many as possible.
There are other learners, too. Some people may be learning the digits of pi as part of a charity fundraising event or as a result of a challenge at school, but whichever group you belong to you will need to choose a technique to memorize pi.
Daniel Tammet is the European record holder for reciting pi from memory – he listed 22,514 digits in just over five hours. He is a savant and describes how each positive integer up to 10,000 has its own unique shape, color, texture and ‘feel’ in his mind. Here we will be a little less ambitious and describe how to memorize pi using word and sound substitutions in a way good enough for you to retain several hundred digits.
This involves using a language which is known as ‘pilish’. In pilish, a number in pi has an associated word with the corresponding number of letters. This language is used to write out sentences in “pilish. These can be linked to form a piece of prose or a story. There are a number of well-known examples such as:
“May I have a large container of coffee beans” represents 314159265
There is a very well-known example where Mike Keith wrote “Cadaeic Cadenza”. This is a short story of 4,000 words which encoded 3,835 digits of pi. He refined the method further to use words of more than ten letters to represent specific strings of digits. Going even further, he collated this with a series of other items into a book which when worked through sequentially uncovers 10,000 digits of pi.
Writing Prose to Memorize Pi
To memorize pi, you can pick an ‘off the shelf’ piece of prose – such as “Cadaeic Cadenza” – or you can write your own, though it has to be said that this latter approach can be quite challenging. Then all you have to do to memorize pi is to memorize the story. When reciting the digits of pi using this method, you have to visualize the word and translate it to a number. That puts an extra step into the retrieval process for each digit.
This technique is aligned to that of ‘piems’ – the poetic equivalent. Just as most writers would say that poetry and prose are as unalike as chalk and cheese so it is with piems and prose written in pilish. Prose can by quoted almost continuously, but poetry has both horizontal vertical structural dimensions which gives even more opportunity for encoding the digits of pi. Therefore, ‘piems’ is the subject of a separate article on the techniques for memorizing pi.
How to Memorize Pi By Grouping Digits
There are five or six methods for memorizing pi, that most well-know of irrational numbers. Which method works best depends on the way an individual’s brain is wired. Some people prefer sounds, others visualize digits and others use a range of memory techniques. The method described here uses the technique of grouping digits to memorize pi.
First, you need to find a calculation of pi so that you have access to the list of digits – how many are you aiming for? For a modest target (say up to 50 digits) the simple method is fine.
- 1. Split pi into small groups of digits (e.g. 4, 5, or 6 digits). Work with a group size that suits you (many people easily remember telephone numbers in groups of four). Once you have settled on a group size then print out the list of digits in a format that suits you. Use pencil to mark the groups. For example:
(3.14159) (2653) (5897) (9323) (8462) (6433)
- 2. Focus on memorizing the ﬁrst small group of say 6 digits (this starting block is easy).
- 3. When you have rehearsed the ﬁrst group, move to the next and practice for a few minutes.
A disadvantage of the simple coordinate method is that if you misremember then you have to start over. If your ambitions are greater, then the advanced method can help you extend the number of digits progressively and also enable you to pick up in the middle of a list.
There are several flavors to this method for memorizing pi, but they generally involve a range of grouping techniques, for example:
- A. One group of 1 (3), 2 groups of 2, 3 groups of 3, 4 groups of 4, 5 groups of 5 and so on, up to 10 groups of 10 (and beyond if your brain is up to it). You can see that this is a series – did you work out how many digits this would enable you to remember? You might prefer just to use this as an extension to the simple method above.
- B. Organize the numbers in the format of telephone numbers (whichever country suits you best). For example – the US (314)159-2653, (589)793-2384, (626)433-8327 and so on.
- C. Building on the previous flavor you can even put names to them so that they read like a telephone directory. Alan (314)159-2653), Bob (589)793-2384, Chas (626)433-8327(that’s 260 digits.
Directories and Music
Going further, you can have one directory for friends, one for famous bands or musicians, and so on! Even with Z you can have Zach and ZZTop!
Some people find that singing helps them to remember – if you have a favorite tune that can help. Pop music is usually in 4/4 time which provides a good rhythm although you may want to shift time signatures as you work with larger groups of digits. That’s expert level!
Finally – Be Practical when Memorizing Pi
Rehearse, rehearse, rehearse, that is the key and it helps to have the digits grouped on cards to make that easy even when you are in the coffee shop, although you may get some strange looks! And if you want to go further, there are even more refinements to take you from expert to master level in memorizing pi.