Engineering Memory

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Engineering Memory

Thoughts on learning to memorize the first one hundred digits of pi.

Published
21 December 2024

About three years ago, I memorized the first one hundred digits of pi. I did it on a lark, after reading Joshua Foer’s Moonwalking with Einstein. The book’s
central claim is that nearly anyone can achieve seemingly super-human feats of
memory with proper technique and deliberate
practice. Intrigued, I put the some of the
techniques to the test and found that they worked surprisingly well. But they
did not just work. They converted the hard and shapeless problem of how to
remember into a problem of discipline and methodology. Remembering became engineering.
The central insight behind most memory techniques is an observation: the human
brain is not bad at memorization per se; it is only bad at memorizing specific
kinds of information. For
example, you can probably only hold 5-9
objects
in short-term memory, but you can visualize your childhood home with relative clarity. And most adults have well-developed memories for certain
topics, such as a car mechanic for car engines. In absolute bits of information, we can hold a lot in our minds, but we
struggle when that information lacks meaning or context.
Memorization techniques harness this observation with a method called
elaborative
encoding. The basic idea is to associate hard-to-remember objects with easy-to-remember
objects. Perhaps the most famous example of this technique is called the method of
loci. In this
technique, you place objects you want to remember in a visually familiar place
called a memory palace. And then recall is just the act of “walking”
through a memory palace in your mind and visualizing each object.
To memorize digits of pi, I used a more modern and advanced technique designed
specifically for memorizing numbers, called a
person-action-object (PAO) system. In a
PAO, one associates each digit in the set {00,01,02,...,99}\{00, 01, 02, ..., 99\}{00,01,02,...,99} to a person doing an
action to an object. Then any six-digit number one wishes to memorize is encoded as the person from
the first two digits doing the action from the second two digits to the object
in the third two digits. I’ll call this combined image representing six digits a “glpyh”. For example,
in my memory palace for pi, I have the glpyh: Albert Einstein
twirling a leotard. What number does this represent? Well, in my PAO, I have
the following mappings:

505050 is Albert Einstein smashing a clock
282828 is Anubis twirling a staff
848484 is Fabio wrestling in a leotard

So in my PAO, Albert Einstein twirling a leotard is the number 502884502884502884. PAO systems
are powerful because they automate the process of coming up with elaborative
encodings. And since you have one hundred persons, actions, and objects, you
have one million unique and ideally memorable glyphs.
That’s basically it. Conditional on already having a PAO system memorized,
memorizing one hundred digits of pi is pretty easy. I think I did this in roughly an hour. I may be underestimating, but it was shockingly fast. I definitely did it in a single sitting. This is because one hundred digits is only
seventeen glpyhs. These fit into a
relatively small memory palace—in my case, in the apartment of an old friend.
Obviously, the harder task was memorizing my PAO, since that requires memorizing
one hundred “base” glpyhs! In fact, probably the
single most time-consuming task of memorizing pi was not even memorizing my PAO
but simply building my PAO in a spreadsheet. This is because each person,
action, and object should be memorable and unique. For example, my
PAO contains both Keira Knightley (777777) and Natalie Portman (222222). If I were
to decode a glpyh with one of them too quickly, I might confuse the two. But I would
not confuse them with Darth Vader (171717) or Serena Williams (060606). So each set of persons, actions,
and objects should be maximally dispersed. (If I could build my PAO again, I
would not include both actresses.) Memorizing my PAO took a bit of time, but I just used Anki cards on
my subway commute. I committed to the bit because I figured having a system for
memorizing numbers would be useful long term. (It’s moderately useful.)
This all might sound like a lot of work, because it was. But for me, the remarkable thing
is that the process converted memorization into engineering. Let me give a few examples
of this.
First, I had a clear process with small, manageable challenges the entire
time. I never really doubted that I would be able to memorize one hundred digits
of pi, but I was surprised at how easy the final encoding was.
Second, when reciting pi, my errors are always
“local” in the sense that they are isolated to a single glyph. The most common error is that I
decode a glpyh incorrectly. For example, I memorized my PAO by putting it in my
childhood home. And I put each decade of my PAO into distinct areas of that
home. So when decoding Albert Einstein twirling a leotard, I might accidentally decode
“twirling” as 383838 instead of 282828. This is because the PAO glpyhs for the twenties and
thirties are in adjacent rooms in my house. I would estimate that nearly all of
my errors when recalling pi involve getting a single two-digit number wrong by a
decade. Contrast this with other forms of memorization, such as putting pi to
music or brute-force memorizing a poem. Here, if you get tripped up, you might struggle to remember where you
were or forget entire chunks. In the worst case, you have a “global error” and must repeat from the
beginning. This kind of global error has never happened to me with pi.
Third, while recalling pi, I can stop at any point, take a break, and then
resume. This is because “pausing” amounts to stopping in my memory palace. Again, contrast this to if I had
memorized pi through a song. I suspect I could take a pause on the order of
weeks. What I would do is take the next glpyh and store it in a new palace
representing the pause point.
Fourth, I can go backwards easily. I simply walk through my memory palace for pi
backwards, which is trivial since I’m just visualizing my friend’s
apartment. Then for each glyph, I decode it backwards. For example, the last glyph in my
one hundred digits is Serena Williams nibbling on a plastic
leg. That’s 067982067982067982. (Technically 828282 is extra if we’re counting “digits of pi”
as digits after the decimal point.) And since “plastic leg” is 828282, I simply say “282828” while
decoding. So I can go backwards nearly as quickly as going forwards because I
only ever need to flip two digits at a time.
And finally, this system scales. Memorizing the first one hundred digits of pi only
required seventeen glyphs. Memorizing another seventeen glpyhs doesn’t seem too hard. I don’t feel like my memory has been taxed yet. Using this system, I think I could memorize a thousand digits of pi
relatively straightforwardly. Honestly, the hard part would be
deciding on the right set of memory palaces and then “jumping” between these palaces in the correct
order. I would probably use an organizing system for my palaces, such as ordering the palaces
east-to-west in physical space. But again, this wouldn’t be “hard” in the sense
of a vague or amorphous challenge. It would just be a lot of work for rapidly
dimishing returns.
So that’s it. That’s how I memorized one hundred digits of pi. If you think it
sounds like a lot of work, that’s actually my point. My
point is that there was no magic here. I came to this process with an average
memory, and average memory is all I have. It’s just technique and practice.
Of course, you might ask why I did this. Everyone I’ve told about it certainly
has. Of course, the trite answer is: why do anything? Besides eat, sleep, and
have sex, humans need to do very little to survive as a species. But my more serious
answer is this: nothing has more positvely impacted my own life than my ability to
change how I view myself and my relationship to the world. We all limit ourselves in our imaginations. One might think, “I can’t do this because I’m
not an X person”, but those beliefs are often grounded in a handful of early
experiences which are then rarely interrogated. My claim, echoing Foer’s, is that basically any person with an average memory can memorize large amounts of information with simple,
well-established techniques. And at least for me, truly internalizing that belief
through experience has changed how I view my own mind.

The process of memorizing the first one hundred digits of pi was presented not as a feat of innate talent, but as a problem that could be transformed into an exercise in engineering through the application of specific methodology and discipline. The author posits that the limitation in memorization stems not from the brain's inability, but from the type of information being encoded; the human brain struggles with information that lacks meaning or context. This led to the development of elaborative encoding techniques, which involve associating difficult-to-recall items with those that are more readily accessible.

The author details a specific technique termed the method of loci, which involves establishing a visual memory palace where items are placed in physically familiar locations, and recall is achieved by mentally navigating this space. This concept is advanced in the text through the development of a Person-Action-Object (PAO) system, a method specifically designed for encoding numerical data. In a PAO system, each digit or sequence is linked to a unique person performing an action on an object. A six-digit number, or glyph, is formed by chaining these associations, allowing for the automation of elaborative encoding. This structure is powerful because it facilitates the creation of a large number of unique and memorable glyphs, suggesting that one hundred persons, actions, and objects could yield one million unique encodings.

The application of the PAO system to pi involved creating specific associations, such as Albert Einstein twirling a leotard being encoded as a specific sequence of digits. The ease of memorization for the one hundred digits was linked to the system's capability to handle large amounts of information efficiently. The author stresses that the true success lay in the process itself, which converted memorization into an engineering discipline rather than relying on some magical ability.

Several characteristics of this process demonstrated its engineering quality. First, the task was broken down into small, manageable challenges, which maintained a sense of control and reduced doubt throughout the process. Second, errors during recall were localized, typically involving only a single glyph, which contrasts sharply with memorization methods like music or poetry where a single mistake can lead to a global failure. Third, the system allowed for temporal flexibility; pausing in the thought process equates to pausing within the memory palace, enabling the user to stop and resume recall at any point. Fourth, the system facilitated rapid backward recall, as walking through the memory palace in reverse allows for quick decoding of the encoded elements.

Furthermore, the system demonstrated scalability. The memorization of one hundred digits only required seventeen glyphs, suggesting that the system is robust enough to handle significantly larger sets of data, potentially enabling the memorization of a thousand digits. The author concludes that this process relies not on inherent memory gifts but on established techniques and consistent practice, asserting that anyone with average memory possesses the capacity to memorize large amounts of information through well-established methodologies. This internalization of the capability has, for the author, led to a profound shift in self-perception and their relationship with the world.