Do you use "reverse lookup"? #MPRL

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?!?

0 voters

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. :wink:

\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.


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.


Interesting post, and I like the expanding sections!

Dominic O’Brien has a similar approach to the year codes, putting 14 or 15 people into each of 7 rooms.

Another example, perhaps, is the way he places foreign vocabulary words into different parts of town based on their gender.

In both cases, the location has a meaning rather than simply being a place to store information.

I think this approach works well whenever you have a smallish number of discrete values to memorize for each of a large number of items, and the order of the items doesn’t matter.


Oh okay… never read his books. Yeah, it’s 15 for Monday/Wednesday and 14 for the rest. So does he also associate rooms with things that remind him of that particular day… or how does he differentiate; i.e., knows the number for the room?

Aside from Sunday at home, Monday at work, I also pronounce it wetness-day (at the pool), and thirsty Thursday (at a bar). Basically, a mnemonic association between palace and weekday.

True, similarly with Alex Mullen when he places the initial sounds of the Chinese words he’s learning. I’ve also read that @LynneKelly is doing the same but with the radicals instead of sound:

I do something similar with book chapters (whenever they are meaningful) and the house/shop stands for a chapter and the inside for the key points of that chapter… works with any nested list though.

It’s certainly easier with a smallish number but as with the radicals example above, you can do more if you got a good mnemonic link. I did Toki Pona once by palace\over{initial\space letter}, but only because the number of words in the language is about 120. Otherwise, I’d use something grammar or script related, rather than alphabetical order, but Toki Pona is also genderless.

I keep the order of the items just in case. The weekday calculation itself doesn’t require it, but if the question changes to: when will date x be on a Thursday again? All you have to do is follow the journey of the palace you already identified as date x’s year code.

Both those cases I’d consider either an exception to the rule or an advanced technique though… and your definition is pretty spot on. Thanks for sharing.


He uses the rooms and garden of a single house. He incorporates a number-shape image into the scene to represent the year code for each room. For example, 0 is a football in his number shape system, and the garden is the “room” for year code 0, so he imagines a large football in the garden. The bedroom is the room for year code 1, so he includes a telegraph pole (1 in his number shape system) there.

I like the idea of everything being contained in a single house, but your idea of associations is nice too.

Maybe those ideas could be combined:

  • Sunday = garden
  • Monday = home office
  • Tuesday = chews-day (dining room)
  • Wednesday = wetness-day (bathroom, or pool area)
  • Thursday = thirst-day (drinks area)
  • Friday = fry-day (kitchen)
  • Saturday = sit-day (living room)
1 Like

I see, so he’s not really making use of the palace itself. Personally, I always found single digit images a little wasteful and rarely if ever use them… football could be used in a 3-digit major system as 819. Same image with 3x the information encoded.

Depends of course on what you’re aiming for. I’m currently at \color{blue}30{dates\over{min}} put differently \color{blue}2{sec\over{date}} and I’m trying to double my speed before the Mental Calculation World Cup next year. As far as I’m concerned, every single step that is not needed should be removed from the algorithm.

Also, and similar to his per room image I got a Mars candy bar as part of my Tuesday palace. This way I know that Tuesday in Romance languages is related to Mars as in mardi (fr), martes (es), and martedì (it). Same then for Venus on Friday, etc… so that image serves a different purpose in my set of palaces.

It’s getting a little crowded already now that I’ve added the double-digit squares to the original images. Luckily, those 7 palaces have been used a couple of times per week on average for the last three years. In terms of memory, the imagined objects in the loci are almost as solid as a real memory.

I can appreciate the compactness of things this way. I got all my digits of pi stored across Paris and no other cities… it does keep things tidy. However, and back to my speed issue, I find the themed palaces easier to distinguish. Not to sound esoteric or anything, but the loci in each palace sort of have an aura of that particular weekday. I don’t think I’d be able to get that with rooms in the same house.

So obvious that it didn’t come to mind three years ago. Went ahead and made it German, so that it’s “tu es” (do it) as in “just do it” and then with the Nike association it’s the local running track. Funny coincidence when I placed the squares… 52^2=270|4 and 270 = NKS turns out to be Nikes. :wink:

All in all, six palaces are within a 10 mile radius and Saturday is the satellite way out at the airport. Don’t you think that if you really start pushing for speed it becomes more likely to confuse a dining room location with a living room location than a running track and an airport?

1 Like

It seems like an interesting idea, but I honestly don’t know what you’re really talking about in terms of general application. Can you offer any examples that don’t involve date calculations? Or is that the only area where “reverse lookup” has any relevance?

Sorry, but the minute you introduce math, my brain just shuts down and I can’t work through it at all. :frowning:


Sure, the reverse lookup is not limited to date calculation. As far as the general application is concerned @Simon summarized it nicely already.

So let’s say you want to learn German and your first language is English. Grammatical gender in English is only relevant to 3rd person pronouns: his gender, her gender, its gender. Almost all inanimate objects are neuter though; exceptions are metaphorical gender such as boats (feminine).

So, there is a vague notion of the concept in English; however, no way of knowing why in German:

  • the CD is feminine
  • the tv is masculine
  • the radio is neuter

So rather than learning these and other words in order and adding a pink bow or whatnot reminders to each individual item, you can just have a set of three distinct memory palaces. Then you can place everything feminine in one, masculine in another, and neuter in yet another palace.

The order you put the items into the palace doesn’t matter, you just want to be able to recall the palace that a certain item is in, in order to determine its grammatical gender. The main point of this reverse lookup technique.

In a way, it facilitates grouping in a way that a pivot table in Excel does; and when you double-click you get to see all the items in that subcategory. The difference is that you already established which groups to use and can’t try different ones like in Excel.

Instead of grammatical gender, you could have used Chinese radicals for learning Chinese characters as describe earlier on in this post. The real advantage though is when you compare it to the options of attaching pink bows, blue ribbons, or whatnot as gender markers… it will just become repetitive very quickly and things might get mixed up because the association is made per item.

The train is der Zug (m) but the tram is die Straßenbahn (f). Unfortunately, you can drop the Straßen- (street) and just have Bahn (f) which is then the same as Zug (m). Der Kuchen (m) and die Torte (f) which are cake and pie. Das Bier (n), der Wein (m), die Cola (f)…

…much less confusing than attaching a logic to each item is to simply reverse lookup where you’ve stored the moon and just deal with the fact that der Mond is masculine in German, even though you know from Spanish that la luna is feminine.

1 Like

I appreciate the additional detail, but, for some reason, your explanation didn’t help me understand what you’re getting at at all! :slight_smile:

I think perhaps I’m not understanding your use of the phrase reverse lookup. I’m used to hearing this phrase in the context of phone numbers: Instead of finding a phone number by starting with the name you want to reach, you use the phone number to find the person. So: two pieces of information, each of which allows you to get to the other. But your examples seem much more complex or specialized than that:

You might as well have written that entire paragraph in German! (Which, in case it’s unclear, I do not speak.)

I don’t want to labor this, since apparently it’s resonating with others here. And maybe I’m reading something into “reverse lookup” that you didn’t intend.


1 Like

I think what the “reverse lookup” idea is getting at is this:

Normally, when you memorize something, you place an image at a location. To recall, you mentally go to the location, and see what’s there.

With the reverse lookup, you start with the image, and then think about which location it was in. The location itself gives you the information you are trying to recall, based on a rule you have defined in advance.

Let’s take another, hopefully simpler example - suppose you want to memorize the political party for each of the presidents of the USA.

The standard approach would be to come up with an image to represent each president’s name, and make that image interact with another image that represents the political party (maybe a donkey for Democratic, an elephant for Republican). You could place these images along a journey with 45 locations.

The “reverse lookup” approach would be to use one large location (e.g. a room, or building) to represent Democratic, and another large location to represent Republican, and put all of your president-name images into one or other of these. At recall time, you start with the image for the president’s name, and remember which location it was in. The location then tells you which political party the president was in.

Hope that makes sense.


Let’s say the three of us go to a game show about the US presidents and these are the different setups we’ll use:

  1. @RMBittner: Single journey with 45 locations (chronological order) with one president per location. Some additional information such as party affiliation, age when inaugurated, etc. also encoded in each location.

  2. @Simon: 2 journeys with one president per location. Some additional information per location, except for party affiliation which is given by the memory palace in which you find the president.

  3. @bjoern.gumboldt: 4 journeys for less than one, one, two, and more than two terms in office. Some additional information in each location.

How many presidents did not complete their first term? Even if you have assassinations, illnesses, etc. stored as additional details, you’d still need to go through your entire list. I could even tell you which ones by just going to that palace in my setup.

Who was the next democratic president after Woodrow Wilson? Even though you’d be able to just check the next and the next until you get to FDR, for @Simon it will simply be the next one in his democratic palace.

Who was president before Chester A. Arthur? For you it’s just one location back on your journey. @Simon and I would need to double check the president’s ordinal number and then see if we’re lucky and he’s in the previous location or if we need to check other palaces.

I prefer the “terms in office”-approach because it involves the most math otherwise. I just find Eisenhover in my 2-terms-palace; whereas, you’d have to retrieve his inauguration date and that of the next president and compute the difference. We commonly call him the 34th president and not 34a and 34b, so that information is the one that is usually the least known.

Fact of the matter is, the one attribute you pick for your palaces comes for free. You will always have 45 locations, but by breaking down the ONE big palace you can tremendously improve upon recall time for that particular attribute. The jumping across palaces to find the chronologically next or previous that @Simon and I need to do is well worth the tradeoff.

Not all all, that is exactly what I mean, but it’s not just “two pieces of information, each of which allows you to get to the other.” like you say. You can always go through your chronological palace and simply call out the presidents that are Republican and skip over the ones that are not. Difference is that you’d have to do this every time, what @Simon describes takes care of this during initial setup.

Maybe that’s the problem with the term though. In the post I refer to it as Memory Palace Reverse Lookup instead of just reverse lookup like I do in the title. You’re right, a reverse lookup could always be done, so maybe I should have even called it Memory Palace Reverse Lookup SETUP, because how you cluster your set of memory palaces determines their efficiency later on.

Ultimately, it’s up to you which piece of information you’d like to give this special treatment. Marianne Williamson’s 12 palace setup for the presidents might well be Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius and Pisces. :wink: I’m sure this reference will be dated before soon, but you now what I mean.


It does! Thank you! And thanks, too, @bjoern.gumboldt, for bearing with me on this one! For some reason, these presidential examples click with me in a way that the numbers/dates did not.

While I am drawn to this kind of dual-layer (or more) categorization, I can’t help feeling that “reverse lookup” is not actually improving anything, just redefining our priorities. For example, I currently have memorized no additional information about the presidents other than their names and chronological order. If I were to re-memorize that list, separating them by political parties, I would lose quick access to their chronological order, since I would have to add an additional layer of “order” information (i.e., number pegs) and then bounce between two or three palaces to find who’s next in that order. I rebel against that, since it’s unnecessary in a purely chronological system and would add a layer of imagery that doesn’t really pull its weight (since it’s just telling me who’s next). The alternative, of course, would be to also maintain a separate, chronological palace. But at some point I would have to ask if what I’m gaining with RL is worth the extra energy.


1 Like

Well, lets not fall into the trap of inductive reasoning though. I’m happy that the presidents managed to get the concept across, but that doesn’t mean they were a primary example of when this technique is useful. You didn’t like math and didn’t know German is how we got there… All birds are animals, but not all animals are birds.

No need to rebel :wink: , you are completely right… in a purely chronological system this doesn’t make sense. Also, it’s always hard to argue for something to be re-memorized.

So instead of re-memorizing, I just hope you didn’t do Shakespeares’ plays yet. The obvious, I’ll leave it to the palace to tell me… comedies, histories, and tragedies (#MPRL). What would be the advantage of putting them all into the same palace? Same number of loci this way and one answer for free via the palace they’re in.

If you do want to know when a particular play was written, then I suggest you just use a 3-digit code with the year. It’s safe to drop the 1 because they where all written between 1500 and 1700. That’s basically how historic dates at competitions are done.

1|594 = LPR in major, so let’s make that LaBoR as in Love’s Labour’s Lost and greates love story in the world is Romeo and Juliet, which takes place in Verona, so Two Gentlemen of Verona is the third play written in 1594. Of course to make it memorable you call the second “gentleman” Jules and it’s basically the same-sex retelling of Romeo and Juliet.

1|600 = JSS, Hamlet, Prince JeSuS of Denmark… just make sure you translate back the title before saying it. So you add the year into the actual title and split the plays across three palaces according to genre. Not sure how that is not “improving” but merely “redefining priorities”?

Also, let’s not forget that my initial example was… how do I know which number between 0 and 6 belongs to this year between 00 and 99… and by doing nothing more than taking my already existing PAO and placing it across seven palaces, I got the answer by simply doing a reverse lookup of where my 2-digit image was in this set of seven palaces.

Now every time I’m doing calendar calculation, I am reinforcing my PAO system, and every time I practice my PAO (in their palaces) I am reinforcing my calendar calculation.


Yes, the presidents example only works properly if there is an assumption that the only thing you want to learn about the presidents is their political party. If you want to know the chronology and other facts, as most people typically would, it wouldn’t make much sense to split them by political party.

Here is a purer example: you are a teacher, and every child in your class is in one of three teams - red, yellow, or blue. You want to know which team each child is in without having to look it up.

Method A: associate each child with something that represents a color.

Method B: create a mental room for each color, and place each child in the appropriate room.

Both methods would work fine, but method A involves a lot of repetition of the color images. Method B avoids that.

1 Like

This made me smile.


A post was split to a new topic: How to do calendar calculations

I suppose in a way this also falls into the same category, even though it’s not the palace itself that gives you the answer directly as it does in the weekday calculation; however, it does tell you where you are in your palace to be able to find the 5 digits before and the 5 digits after the current location.

1 Like