Hathaway

Ponders - Memorising Pi to 1000 places

When you are introduced to the idea of Pi, it seems quite simple on the face of it…….. just a relationship between the diameter of a circle and it’s area. It becomes far more interesting when you are first taught at school that it is an irrational number – in other words, not simply something approximating to 3.14, but in reality a number with a random, non repeating decimal expansion that seems to go on forever.  The furthest that our super computers have taken this so far (2024) is 202 trillion decimal digits.

After spending a lot of time looking for (and, unsurprisingly, finding no) patterns in published expansions of Pi, my attention was caught by reports of people testing themselves by trying to memorise it as far as they could.  

That’s it…. I  was hooked. 

My initial attempts, using  brute force memorisation, were not all that successful and it soon became apparent that a more systematic approach was required

Enter the Major System

I went to school in Tunbridge Wells where there is a lovely old bookshop near the famous Pantiles called Halls  (still there to this day,and still wonderful). An old book on Codes from there was my introduction to the Major system, being a six hundred year old mnemonic technique that helps people memorise numbers by converting them into words and images, based on the idea that people can remember images (the weirder the better) more easily than numbers, then convert the same back to numbers when required.

It works by linking consonant sounds to numbers in the following way:

[1 = t/d/th ]  [2 =n]  [3 = m]  [4 = r]  [5 =l]  [6 = sh/ch and soft ce/ge as in voice/cage]  [7 = g/k and hard c]  [ 8 = v/f/ph]  [9 = b/p] and [0 = s/z]

All vowels are ignored, together with h, y, w, and any other letters that are silent. Double letters as in the word ‘all’ for example will be treated as one i.e. ‘l’.

So, my name ‘Mervyn’ can represent the number string 3482. Then,  if I manage to forget the number 3482, all I need to do is to remember my name and convert the consonants in it back to numbers via the Major System. This is the underlying principle of Pi Memorisation.

Wikipedia now has a good article on things Major, it which probably gives a better explanation than I have done, and you can see it here

Mapping Pi

My approach was to regard the first thousand decimal digits of Pi as 100 blocks of 10 consonants, and construct a sentence for each separate block to record the encoded consonants – the idea being that our brains hold words / images much more efficiently than mere numbers and that these numbers can then be retrieved from the mind, when required, by converting the images back to numbers.  It soon dawned on me that, whilst this was doable, recalling the order of the 100 sentences would be much easier if each was prefixed with a logical and orderly index that itself was an integral part of each sentence

This then is my ‘tweak’ to the Major system and, while I know it sounds convoluted, examples will make it much easier to see.

Compound index

Consider a two part index, at the start of each sentence, where the first part follows a given alphabetic order, and the second part is the Major system phonetic element. 

The first part of my index follows the sequence ABCDESGHNO, where each letter covers 100 numbers

The second part of my index follows the Major system phonetic sequence t/d, n, m, r, l, sh/ch/j, g/k/c, f/th/v, p/b, s where each phonetic element covers 10 numbers of the 100 number sequence.

So, the first of the hundred sentences will start with a word using a form of ‘A t/d’ followed by the first 10 decimal digits of Pi, being 1415926535.  In other words, [A – t/d]1415926535, which for example can be converted to:

[Ate] TuRTLPie, a NiGeLla MeaL

The second of the hundred sentences needs to encode the next ten digits of Pi as follows:

[A-n] 8979323846 which could be, for example [Any] PHoBiC PieMaN May FoRGe

So there it is…. This process needs to work its way through [A t/d] to [A s], then [B t/d] to [B s] and so on and so on, where each Alpha part of the compound index will account for 10 sentences, each of which houses 10 digits of Pi.

In this way, not only will you be able to memorise large sections of Pi, but will be able to keep it in the correct order.

Imagery

The above two example sentences are just that: examples. You will need to construct your own imagery that resonates with just you and no-one else; and the sobering fact is that we are more likely to remember imagery that is violent, surreal, screamingly funny or just downright pornographic! Constructing the sentences is a fun part of the process.  

I hope you have fun with this. When originally experimenting with Pi memorisation I took it to 1000 digits……. but there is no reason for you to stop there if you are up for it……. just keep increasing the first part of the compound index sequence, and continue applying the Major system to the second element – then let your imagination run wild!  

Last words

This may all sound daunting, but is it any different to actors learning lines for a play?….. at the end of the day, a thousand digits of PI = 100 sentences where the first word of each sentence follows a strict order and almost acts like a prompt. 

One of the further benefits of the compound index is the ease with which it allows you to quickly locate a specific section of Pi. For example, to answer a question like ‘what is the 464th decimal digit of Pi?’ Well, you know that the first part ‘D’ of a compound index covers the range of digits 401 to 500, and that [g/k/c] will be the second, phonetic, part of the index which covers the seventh of the ten groups of ten under ‘D’, in other words the 461st to the 470th decimal digits of Pi.

Therefore the answer to the question lies in whatever sentence you have constructed for compound index D[g/k/c].

As the actual 461st to 470th decimal numbers of Pi are 0113305305, and you have already, say,  constructed the sentence:

 [Dog] STaDiuM May SeLL MuSeL

the answer to the original question lies in the fourth Major system element of the above sentence which, being M (i.e . the ‘M’ of the word ‘Stadium’) which  is the number 3 in the Major system.