Numbers and Memory
I do not have a very good memory. I forget names easily, I’ve never been able to remember dates, and I go through phases where I completely lose my chain of thought midsentence and forget what I was going to say.
Ray Dalio in his book, Principles, echoes the same sentiment:
Rote memory is memory for things that don’t have an intrinsic logic for being what they are, like a random series of numbers, words in a foreign language and people’s names (all of which I have trouble with). On the other hand, I have a great memory for things that make sense in a context. For example, I can tell you what happened in every year in the economy and markets since the mid-1960s and how many things work
It seems some brains have a habit of dispensing with any data that is arbitrary. By arbitrary I mean that it could be different and nothing else stored in my brain would need to be updated. For example if I thought somebody’s name was Fred and it turned out it was Michael, in my brain’s web of data I’d only need to swap out one dot for another because there would be no connected dots I’d need to revise.
On the other hand if I found irrefutable evidence that the fuel in cars is purely used to make your car heavier so that the wheels have more traction against the road, I’d need to re-evaluate a lot of shit. Why not just make cars heavier? Through what process is the fuel consumed? Why am I paying all this money on fuel if I’m satisfied with the amount of wheel traction when I’m almost on an empty tank? How come I keep hearing stories about cars not being able to start when they run out of fuel? Why would the US military care so much about oil in the middle east?
Because the dot in my brain that encodes the fact ‘fuel makes cars go’ is linked to thousands of other dots, changing it requires my brain to traverse all those dots and check whether they too need updating, and then repeat the process for all of their connected dots. That’s a very expensive operation and one the brain has no interest in doing (possible implications for why losing one’s religion is such a painful process?).
‘Orphan’ dots such as dots encoding people’s names are more likely to encode useless information than tightly linked dots like ‘fuel makes cars go’, because a link between two dots signifies some logical relationship, and if a dot is logically related to a heap of other dots, it’s more likely to encode something that is factually true or at least useful to the person. So it’s no surprise that people get names wrong all the time, because all else being equal there’s no way to verify the fact through other information you have, except to some small degree that person’s race and gender.
Orphan dots present another problem: our brains have a certain capacity for information, and the more dots we store, the more time it takes to scan them for information we’re trying to recall. Compare this to a hard drive which is near max capacity and whose search speeds are painfully slow. If we unconditionally stored every single piece of information we consumed in any given moment, our brain’s search speeds would crawl to a halt.
So our brains do the same thing that computer programs do: garbage collect. In a well written computer program, if a piece of data is no longer being referred to by any variables, it’s garbage collected so the memory can be used for other data. When a program ends up using loads of RAM, we call that a ‘memory leak’ because useless data isn’t being cleaned up. Our brains also garbage collect for the exact same purpose.
But obviously remembering names is highly useful because it spares us from embarrassing situations, so our brain needs to have some level of mercy on dots that aren’t tightly connected to other dots. We can consciously get around this by visualising the person and repeating the name in our heads so that we create some links and de-orphan the name dot. Maybe we think about somebody else with the same name, associate the two people’s faces in our heads, so that when you’re at a loss you can recall associating person A with person B and then leverage off that dot to recall the name.
So it seems like the trick to remembering things is to find logical relationships between otherwise arbitrary points of data. A concrete example is that my car is in for repairs and I couldn’t recall which of the two buttons on the key locked/unlocked the car, which is annoying when it’s dark and you can’t see the icons on the buttons. The unlock button was closest to the actual metal part, so I reasoned that most of the time your car is unlocked, you’re sitting in it driving it, which puts you closer to the car than when its locked, just like how the unlock button spends most of its time (all of its time) near the metal part of the key. It’s a silly analogy, but it’s impossible to forget because if you walk through the logic you’ll reach the same conclusion each time.
In highschool I memorised the first 100 digits of pi just to see if I could, and if I recall correctly (which I likely don’t because of how poor my memory is) it took me a while to do. My strategy was to just add a few extra digits on each time and repeat the process until I got to 100, but that’s a fairly painful process. Knowing what I know now about how my brain works, I decided to see how easily I could memorise another random string of digits: the first 100 digits in euler’s number e:
e = 2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274
There is nothing more arbitrary than a string of random digits, but my task was to find ways of imbuing these numbers with meaning and logic so that I could trick my brain into thinking the numbers weren’t garbage waiting to be collected.
First step: split into chunks of 5, then split those into chunks of five:
Okay that seems more manageable now. I can just memorise it chunk by chunk and block by block. But it’s still tricky to just take a number like 71828 and memorise that. I need to pile some more meaning and logic onto it so that it feels less arbitrary. Why not harness the geometric areas of my brain?
Okay that’s a bit more easy to reason about. We kind of bounce between big numbers and small numbers, going from 7 to 1, then we continue the bouncing but one unit up so we go to 8, then 2, then back to 8. Next block:
Interestingly here we have the same bounce from 8 to 2 to 8 that we had in the first block, but it’s in the centre this time and it’s surrounded by 1 and 4 (worth noting that the last four digits here are all even).
This one is super easy to remember. You’ve got two step-ups, separated by a gap (0) in the centre. We also finish up the same place we started, on 5.
This one is a bit more squashed down than the others. Ignoring the 2 at the beginning, you have a step up from 3 to 5, then back to 3, then back up again but one more unit than the 5 (getting us to 6). That’s kind of reminiscent of the pattern in the previous block, 59045
Last one in this chunk, we start off at 0 and we only use even numbers for the first half, stepping from 0 to 2 to 8 (pretty exciting). Then we lose our excitement and get tired of using only even numbers, decaying down to 7, then 4.
I’ve given each of these blocks a kind of story, and those stories help lock into place what the numbers are. If I forget that 8 is the middle number in the above block, I can appeal to my recollection that the first three digits are even, and that there is a steep incline as well. Given that I remember 0 and 2 are the first two digits, that means the third can only be 4, 6, or 8. I recall that 7 is the fourth digit so obviously the number can’t be 4 or 6, otherwise we wouldn’t be sitting on the top of the mountain in the middle, so the number has to be 8.
It might be slightly counterintuitive that giving yourself more information to recall can actually help you remember things more, but that’s because your brain cares less about arbitrary data than logically related data. Giving each of these blocks a story helps me inject some of my own arbitrary data that conveniently logically relates to the arbitrary data I’m actually trying to remember (the sequence of numbers). Once there’s logical relationships, my brain’s garbage collection algorithm rocks up to the place I’m storing this data and thinks ‘I’m not touching that, way too interconnected, probably important’, and goes on about its daily life, mercilessly trashing the names of people I used to know.
Anyway I’ve just reasoned my way through a quarter of the first 100 digits, and rinse and repeat: memorising 100 isn’t so hard. I might take ages on a given chunk trying to remember what it is, but having it mentally located in that table of chunks and blocks, and having the story associated with it, I can always eventually work out what the numbers are.
If this little experiment has taught me anything, it’s that although my younger self may have had a bit more mental horsepower, the older Jesse wins on the strategy game (yes, my competitive spirit evens pits me against other versions of myself) and the better you know your mind, the better you get at turning hard problems into easy ones by breaking things up and reframing the chunks into forms you’re better equipped to reason about. Problem solving does not have to be a painful process; you just need to know at what scope pain arises, and then split the problem up and reframe so that the subproblems are sitting just beneath that point.
Appendix: Are the digits of e actually random?
Given that we see the sequence 1828 show up in the first two blocks of e’s digits, it begs the question of whether e’s digits are actually random. In maths, the word we give to such random numbers is ‘normal’. If a number is normal in base 10, then as you take larger and larger slices of digits, you should expect the frequency of each digit 0,1,…,9 to be roughly 1/10 i.e. you should see the digit 0 show up 10% of the time, 1 to show up 10% of the time, and so on.
But you should also expect the sequence of digits 00 to show up 1% of the time, and 01 to show up 1% of the time, and so on. Otherwise you could have a number like 0.01234567890123456789… and it would be considered random, which it’s clearly not. Extending the definition, you would expect the sequence of digits 000, 001, 002, …, 999 to all show up 0.1% of the time. The general pattern is that you expect any n-digit string to show up at a frequency of 1/10^n.
An approximation we can use here is to note that of all the 10-digit strings, exactly 10! have each digit exactly once. 10! = 10 * 9 * 8 … * 1, and the reason it’s 10! is that you pick any number 0–9 to put in the first digit, then any of the remaining 9 numbers to put in the second digit, then any of the remaining 8 numbers to put in the third digit, and so on. So at each digit we’re splitting the tree up into fewer and fewer branches, leaving us with 10! leaves.
Given that there are 10¹⁰ possible 10-digit strings (because when you are allowed to re-use digits, we can go 10 * 10 * 10 … * 10 for as many digits as there are) we would expect a truly random number to have 10-digit long strings containing each digit once (e.g. 1237469850, we’ll call these permutation strings) occurring at a frequency of 10!/10¹⁰, because that’s the actual fraction of permutation strings that occur in the set of all possible 10-digit strings. 10!/10¹⁰ = ~ 1/2755.73. So if we say p(n) is the number of 10-digit long permutation strings in some slice of n digits, we can graph the ratio of n/p(n) against n:
That straight dotted green line is at the 2755.73 mark which represents truly random numbers. Pi is pretty much spot-on so we can confidently say that pi is truly random, but for whatever reason e is sitting a bit below that line, meaning that we actually see more permutation strings in e’s digits than we would in a truly random number.
Who’s to say whether e actually does end up converging on the green dotted line? This is currently an unresolved problem in mathematics, in fact we don’t know whether e, pi, the square root of 2, or the natural logarithm of 2 are normal or not.
