For the younger generation
back in the days we’d see people’s phone numbers on our display and then needed to figure out who’s number it was. Basically, instead of thinking of the person you want to call and then dial their number, you’d do things in reverse; hence, reverse lookup. These days looking up which country an IP address is from would be considered reverse lookup.
So I was wondering… normally, we’d use memory palaces to store information in order (e.g., digits of pi, etc.) but do any of you ever do the opposite of that? A memory palace reverse lookup so to speak.
- Sure, isn’t it obvious though?
- Nope, but will from now on!
- What are you on about?!?
Let me give you two examples where I do it:
Example 1: Calendar calculation
(expand the below for details)
Days to weekdays
If you’ve never done calendar calculation before, have a quick look at May 2000 and May 2023. Both start on a Monday (first day of the week) and for the rest of the days (say 17) you just need to take the remainder after dividing by 7 (length of a week) to get the weekday (17 → 3).
Months codes
Next note that the months simply offset that logic by a value between 0 and 6. August will move things “one in”; February, March, and November “two in”; etc. Simple mnemonics will suffice: A1 sauce (A=August and value=1) at a BBQ in August. April and July are the only two months with an L and conveniently their code is their major system values: 5.
Leap year adjustment
Lastly note that 2000 is a leap year and January and February are “one out” from their 2017 (not a leap year) counterparts. All in all, the formula is: day + month code and -1 if it’s a leap year (if the month if January or February).
Year codes
Now compare what you know with 2001 and 2018 and you’ll find that you need to only add one for the year code and you got the answer. Unfortunately, there isn’t much of a pattern… it’s not like all years that end in 5 have a code of 5 or some logic like that. There are formulas to calculate the date, but then again this is the Art of Memory forum. 
\color{blue}~ Memory Palace Reverse Lookup (\#MPRL) ~
Instead of using a journey with 100 loci and placing the numbers 0 - 6 in them, which will become very repetitive very quickly; I use a reverse lookup instead. For this I take all the years that have an offset of 0 (i.e., 00, 06, 17, 23, 28, 34, 45, 51, 56, 62, 73, 79, 84, 90) and put them into a mini-palace that reminds me of Sunday (value=0). Let’s say on Sundays I enjoy time in the garden.
Monday (value=1) I’m back in the office and I place all years that give an offset of 1 (i.e., 01, 07, 12, 18, etc.) there. Just continue the same for the values 2 - 6 with palaces that remind you of Tuesday through Saturday. This is also nice if you are looking for a daily routine to practice your 00-99 system. You’ll have ~15 values each day (that would appear pseudo-random) you can review.
So now if you see April 9, 2070… you got 5 for April plus 9 to get 14, which conveniently has a remainder of 0. Now you look for where you’ve placed 70 and you find it in your Wednesday (value = 3) palace; and there is your answer.
If you want to be really smart about it and have a PAO system, you place your objects everywhere and only for leap years you’d use your persons. That way you don’t need to additionally go ahead and check if the year is divisible by four to figure out if it’s a leap year or not. If the reverse lookup gives you a person you are looking at a leap year and need to subtract 1 if the month is January or February.
Example 2: Squares and square roots
Now with all your 00-99 images in place, you can attach 3-digit images to them if you are into mental math. Note that your 2-digit PAO and 3-digit major system are mutually exclusive, so there will be no confusion as to which is the square and which is the root.
Memory palace setup
The squares from 99 down to 32 are 4 digits in length, so drop the last digit. The squares from 31 to 10 are 3 digits in length, so drop the last digit and prefix a 0. The squares from 9 to 0 you already know, so don’t bother… or prefix two 0s if you must.
The reason you can drop the last digit is because it’ll always be the unit digit of the square of the number you are squaring. That sounds way more complicated that it is… basically, 0 (as in 10, 20, 30, etc.) will always give you 0 in its unit digit… 50^2=2,500 and 5 will always give you something with 5 in the unit digit 85^2=7,225. Also for 4 and 6 it’s 6; 3 and 7 it’s 9; 2 and 8 it’s 4; and 1 and 9 it’s 1. Absolutely no need to waste loci on that.
\color{blue}~ Memory Palace Reverse Lookup (\#MPRL) ~
Say you want to know 48^2… you just go and find Ric Flair (major = 48 = RF) who has his nemesis (major = NMS = 230) in a figure-4 leg lock. So 48^2=2304. Of course here, the figure-4 is too easy to not use as a mnemonic, but 8^2=64 from the unit digit in 48 would also give you 4 as the unit digit of 64.
The square root is even easier, because instead of calculating the last digit, you just drop it. Say you are trying to find the square root of 5329. Simply drop the 9 and convert 532 into LMN into lemon. Not sure what your image would be (I’m not sharing mine) but Kylie Minogue (73) and lemon go hand-in-hand. Done!!!
In conclusion
Using familiar concepts, we are able to use a reverse lookup by finding the palace (Tuesday) in a set of palaces (Monday - Sunday), instead of storing at ton of repetitive values (0 - 6) in 100 locations. By using a set of palaces we are able to cluster the information.
Of course when reviewing you always see Kylie and the lemon together… and neurons that fire together wire together, so every time you practice your calendar calculation you also practice you squares and square roots (and vice versa). During recall you are not interested in which weekday palace Ric Flair is in and equally you don’t care about his nemesis when doing weekday calculation… but this knowledge is now intertwined.
Discussion
Ever used the concept of memory palace reverse lookup? Does it makes sense to you or not at all? Please vote above and leave your comments below.
