Hi, I’m Woodrow; I’m 28 from British Columbia in Canada.
I’ve been working on my approach to a two card system. It makes a few changes from other systems I been lucky enough to come across online!
I wanted to share because I would like some feedback, and maybe someone will find this post helpful in understanding 2 card systems.
It takes inspiration from Kate Kermode, Lance Tschirhart, Alex Mullen, Johannes Mallow, and Ben Pridmore. The part that is mine is the way I approach the problem.
I wanted to address these issues:
- I wanted every single image possible to “map” directly to a number, even above 1000, with out special cases as much as possible. I want to be able to use as many of the extra 352 images for other purposes, as easily possible. For me, that meant doing my best to arrange the numbers in a linear way on the number line. This system achieves that. 1300 of the 1352 images will map to a number sequentially. These will be numbers 0-1299. They are arranged according to phonetic rules that allow a linear placement, with fewer special cases. There are only “52” card-discipline specific images that do not occur sequentially in a number line. (I call this “the patch of 52”, because it jumps around)
The benefit of this is an increase in usable numbers by 300. Some may find it easier to learn as well, since the system uses fewer phonetic exceptions and to me at least feels more intuitive.
The explanations I’ve seen online of other systems place phonetics as the focal point. For me, I seem more comfortable working in and referring to numbers. Another benefit of this is the ability to plug in different phonetic systems and experiment easily, replacing the number value with the associated phonetic. The image exists as a number first, from 0-1299, with the exception of the patch of 52 images which stand alone. The patch of 52 card-discipline specific images (images not used in 3 digit random number events or binary events) will follow the same phonetic rules, and map directly to a number. However, will unfortunately not map sequentially. I feel the advantage of not changing the phonetic rules is greater than the benefit of an additional 52 sequential images. While these 52 images could be considered as having a number value, they will jump all over the number line. This probably won’t make sense now, but read the whole post. I will also post a google document where can visually see the mapping of images to cards.
I found the systems a challenge for me, personally, to understand and wanted something a bit clearer cut.
3 digit card systems are also used for binary and cards. I wanted to make some small adjustments to the way the numbers map, not a considerable change.
To provide another perspective for others making a 1352 image system.
I wanted to easily explain a 1352 image system, in a way that anyone could understand.
As a small added bonus, in Lance’s system, he uses only 992 out of the first 1000 images. My system will use 1000/1000, and the additional 300 will be usable for other projects. (Admittedly saving 8 images in a 1352 image system is nothing as it accounts for 0.006 percent of the system. It is more speaking to the linear way the system is organized)
My reason for wanting the extra images above 999 in an orderly fashion is to:
learn the system more quickly and easily
encode everyday things with more flexibility
to use as decimals (XXX.00 - XXX0.99
sixteenths of an inch for carpentry, imperial measurements
the alphabet represented numerically
examples: 1000-1099 as a 2 digit system, 1100-1199 for alphabet, etc.
Before exploring this post I would recommend the following:
-An understanding of different base number systems. If you are not familiar with different base number systems such as binary, or hexadecimal or sexagesimal, I would recommend checking it out on youtube. You don’t need to know anything exact, just that the way we count to 10 is a cultural decision and relatively arbitrary. In this 1352 image system, we will kind of fudge a Base13 and Base8 System around for optimal use of images, every 1352 image system does this
-Read Lance’s Post on his system.
-Understand the variable locus principle which is used to turn 16 possible suit combinations (4x4) into only 8.
-Understand how a 52x52 = 2704 image system can be condensed into 1352 images by using the same image twice, and encoding which of two possible card pairs it is by using a variable locus system.
-When I use the term “mapping” I am liberally using what I understand to be a software concept for representing a value, with another. I am not a software engineer, please let me know if this is the appropriate use.
A Quick Over View:
The system is multi-discipline. Meaning it is used for binary, numbers and card events.
Instead of using Lances organization of (Suit, #, #) I will do (#, Suit, #). This is also what I understand Katie Kermode’s system to be.
It is created with multiple memory disciplines in mind from the start. This is important to consider when building your system. It is easy to get started building a 000-999 system with basic major system principles, but you will need to eventually solve the problem of mapping the images onto cards, which do not use a base 10 number system.
A basic principle of building a multi-discipline number system is that you want to use as few images as possible, with as little excess of event specific images as possible, and in a logical and quick to de-code manner.
This system uses a drawn out extended major system with 13 consonants by redistributing the numbers with 2 possibilities such as 1 = t/d for example. It can be used as pure 'extended major’ system. By that I mean creating 3 digits with Consonant, Consonant, Consonant similar to what Lance or Alex use. It can also be used as a Consonant, Vowel, Consonant system, like Ben Pridmore. In that case, it uses what I understand Katie Kermode’s Phonetic System to be, which is based on Ben. Even the though the number of images goes into 4 digits (up to 1352), we will never have more than 3 phonetic sounds to combine. if we used a regular 0-9 major system the number 1202 would be t-n-s-n… or if we imagined the face cards as 2 one digits add as well, then king suit combo jack may be 12310 or t-n-m-t-s. We want to avoid this long languages pieces. They are too difficult to derive images from and the subvocalization you may experience while “reading the card" would be longer as it is more syllables than a distinct sound for every value 0-C (as in base 13).
If using Consonant, Vowel, Consonant you will need 13 Consonants, and 10 Vowels, and in the ones place, the same extended major system is used, however only 0-9.
My approach uses Base 13 labelled as A B C instead of Jack Queen King. This is again because I think of these values as numbers first. The use of ABC as a standard is another way to remember its linear position in a number line. Meaning which is not conveyed with the letters J, Q, K.
In number systems that count beyond 0-9 in one place value, to idea of 10, 11, 12, 13,14, 15, 16 are represented as letters A, B, C, D, E, F for example in hexadecimal. In this way 10 = A, B = 11 and C = 12. This is important because cards are a base 13 system in face value. (Although because every single card is unique it’s really a true base 52 system).
This 52 card system is created using 13 distinct face values Ace-10 and Jack Queen King. These 13 face values will repeat 4 times each across 4 suits. Therefore 13 x 4 = 52.
A 2 card system, by name and nature is all about more efficiently memorizing cards by memorizing them as distinct pairs. 52x52 = 2704 possible card combinations. (Technically 52x51, since identical cards can not occur twice, but let’s not go down this road) This can also be expressed as 13 face values x 16 possible suit combinations x 13 more possible face values. 13 x 16 x 13 = 2704. In this system we half the number of suit combinations using the blocks of 2 pairs as outlined below; for now let us continue on this train of thought. We are making a pair of possible card pairs. Since “a pair of pairs” is confusing language, I will call the 16 possible suit combinations a pair, and the groups of 2 possible pairs as blocks… This is referenced in other posts calling this a “2 Block System”. By making pairs of 16 possible suit combinations (a pair two possible pairs), we end up with 8 possibilities. This yields the system of 13 x 8 suit blocks x 13. 13x8x13 = 1352. This is our number of images in this system.
Now we are presented with a few problems here to solve for.
We only want 3 consonant or vowel combinations, so we use a base13 major system.
The suit combinations are base 8 so anytime one of the 2 numbers outside of our system from 0-9 occur in the tens place, we will not be able to map this number from our 000-999 number system to our card! (I know you would assume these two numbers left out would be linear as well and logically 8 and 9 would be omitted leaving 0-7. Actually, we will omit 4 and 8 to create a base 8 suit system. The reason for this is related to the frequency of certain sounds in English and there is more below. With the two digits left out of the tens place, this results in 2x10 or 20 places per hundred images are not mapped from numbers to cards. From 000-1299 that will be 20x13 = 260 additional images to make; you could also see it as 260 images from numbers you don’t get to practice doing cards, and 260 more images to review. I am too lazy for this. So if we stick with Base13, Base8, Base 13 we will have to create 1352+ 260 = 1612 images. Furthermore, they will not be organized in a linear fashion we can use for everyday base10 number memorization; and to some imagining the card on the number line may be a slight help in learning the card. So these are two setbacks we will tackle next.
There is an easy solution that every 1352 image system seems to use. In the ones place we will use Base 10 Instead of Base13. That means the idea of A, B, C representing the numbers 10-11-12 or jack queen king only exists in the hundreds place. This is great because 10 hundreds can easily be expanded on place value to the left same with 11 and 12. But let’s still call it A, B, C because of their distinct phonetic sounds from 11, 12, 13. We are blurring the lines between 3 digit and 4 digit numbers by using a base13 system in the hundreds place.
This is how you express 13 different values with one place value (don’t forget 0 counts): 0,1,2,3,4,5,6,7,8,9,A,B,C
Card value 10 is mapped to number zero and A B C represents Jack Queen King, or Jack=10, Queen = 11, King = 12. Well let us take Jack and Queens… and map them into the tens place where our values of 4 and 8 are omitted.
Every time you see the value 4 or 8 in the tens place, imagine it is a wild card… or a special card in a game. It doesn’t follow the rules. If you see #,4,# we will do something special. We will let a 4 in the tens place represent a queen as the value of the 2nd card. And for 8 in the tens place we will let it represent a Jack as the 2nd card.
3,4, Suit = 3, 4, (Suit Block)
B,4, Suit = Queen, Queen, Suit
9,8, Suit = 9, 8 Suit
Let’s hold off to learn the suit combinations, but for now I will teach you one. A heart-heart suit combination can be represented by the number 0. So let’s fill out the examples above with that information pretending both cards were a heart.
3,4, Suit = 3, 4, heart-heart
B,4, Suit = Queen, Queen, heart-heart
B = 11
9,8, Suit = 9, Jack, heart-heart
Since every 1st card value can occur 0-C and every suit value (base8) can occur we have mapped a bunch more useable images. To find how many images we can take 13 x 8 x 1 = 104. (Because 13 possible card values, 8 possible suit blocks, and 1 specific jack or queen)This is true when tens place is 4 and again when tens place is 8. 104 x 2 is 208. Of the 260 images not mapped, we have now mapped 208 of them. 260-208 is 52.
The only situation we don’t have a solution for is the very specific case of when the 2nd card value, is a KING. There are 13 possibly face cards which can combine with a King so 13 possibly outcomes x 8 = 104 (same as above). Meaning if you pick one card (like Kings in the 2nd place) there are 104 possibilities that’s can occur. 13 different values x 8 card blocks.
Let’s look at the way the King rules work, and then we’ll return to mapping the last images.
It works by creating a false base11 system out of a base10 system by using an omission. (This is a real stretch of these terms, and may be over complicating, but you can simply think, "When KING is 2nd, we have no value to express it, and express by an absence of value. An omitted value is not the same as a 0 because zero has a phonetic sound and an omitted value does not. Digits 0-9 can occur + an omission of the ones place. In a situation where a king is second, the result will be a 2 digit number.
K, K, (heart-heart) = C, 0, (king omitted)= C0. Note again the difference of 2 digit place value representation of a 3 digit number as C0 is really 120 with a different consonant. the zero is because we are sticking to our heart-heart example)
2, K (heart-heart) 2, 0 (omit) = 20
6, K (heart-heart) = 6,0, (omit) = 60.
Again note: 20 is not the same as 020 and 60 is not 060. This 2 digit number will result in only 2 consonants. Or a consonant and vowel. 020 would be phonetically s-n-s. 20 is only s-n. This could be the difference between snails or sin. Again there are 2 distinct images. In the same way, when a face card is first. B(Queen), 0 would be considered B0, not 130, or 0130. B, while in numeric value the same as 11, has a different phonetic rule. Number value B is the sound “d”, while 11 is t-t. Therefore B0 is d-s and 110 would be t-t-s. Two completely different images would result.
The explanation I give here is round about and long winded. I’ll give you a peek at the eventual solution we will arrive at now. We have52 remaining values from 000-C99 and 104 remaining card pairs to map to images. These are the images for 2nd Card value = King, which can occur 104 unique ways. 104 doesn’t divide by 13 (the number of possible face values) nicely. So we will instead divide the king combinations by suit block possible outcomes(8). We will place 4 possible suit block outcomes within the 000-C99 completing that linear system, with every number mapped. The remaining will be the 52 card specific images, which can be considered as having number values following the phonetic rules, however they jump around.
I have not decided on my phonetic system yet… I am still experimenting, but the benefit of mapping like this with numbers, is it is easy to replace the numeric value with a sound and the entire system has changed, since numbers are the base of the entire system.
If we did not use the digits ending in 44, 48, 84, 88 we would lose 52 values, not have a linear system. We would however be able to only have ONE King 2nd rule, being drop the Kings Value and express it as a 2 digit number. That one rule would hold up every time, but we would have to create an additional 104 images which would be card specific, and we would not have the advantage mapping every card to the number line in a linear way.
With this ONE king 2nd special case rule, It would be a 1456 images system. Not maximum efficiency, or use for other daily memory tasks.
So we have another problem to solve. How to map half the 104 images to our empty 52 images from 000-C99 that occur when the tens and ones value are 44, 48, 84, 88 (occurring every time the hundreds value changes from 0-C. 13 hundreds place values x 4 = 52 images.
We will map half our remaining values to the 52 numbers missing from 000-C99 (aka 000-1299). Then every image will be used on the number line 000-C99, and we will add an additional 52 images for a total of 1352. At this point, the image mapping will be complete.
The most reasonable way to halve the possible King 2nd outcomes is to pick half of the 8 card blocks to map to the images linked to numbers less than C99/1299 and pick 4 card blocks above C99/1299.
First let’s examine which numbers images are are not yet mapped, less than C99.
If you feel a bit confused, just keep re-reading and breaking the system down piece by piece. A 1352 image card system is a bit like a rubiks cube. Each layer you solve gets progressively harder. But here we are at the last "layer”. The the system is solved.
I would recommend taking a break before we move on.
Picking back up:
I think of 4’s and 8’s as being almost like wild cards in a game… all the special rules and related to them.
If in the tens place we have a 4 or 8 and it is followed by a number in the ones place that is one of our suit block numbers (anything but 4 and 8), we know the 2nd card is a queen or jack. If the 4 or 8 occurs twice, in both the tens and ones place, we will know the 2nd card value is king.
So let’s assign suit values to these following combinations of the tens and one places.
I made these choices based on vague visual associations I had. To me a repeating digit reminded me of a repeating suit.
44 will represent heart-heart/spade-spade
88 will represent diamond-diamond/club-club
And since 44 is heart-heart/spade spade, I consider a 4 to represent hearts or spades. 88 represents diamond-diamond or club cub so I think of 8 representing clubs or diamonds.
I decided to go with the same color suits of 48, 84 instead of red and black color. This means any same suit block with king 2nd will be in this special case, and any mixed color combo will use the other special case king 2nd rule.
48 will represent heart-diamond/spade-club (notice the 4 is the heart, from 44 and the 8 is the diamond from 88)
84 will represent diamond-heart/club spade (notice the 8 is the same color from the 88 pair. not sure this is making sense, let me know if you need clarification)
Here I will repeat myself and give the complete list:
44 or 0 = or
88 or 7 = or
48 or 6 = or
84 or 2 = or
The only remaining suits digits in the ones place are: 1,3,5,9
Convenient to remember because they are all odd. and are all of the mixed color pair blocks.
Now every image 000-1299 is mapped.
The remaining 52 i call the “patchy 52, or non linear 52” because they aren’t sequential and occur from 00-C9 (120) in patches and skips.
Any digit 0-C can occur in the tens place. But the only ones place digits that can occur are 1,3,5,9.
01,03,05,09 are the possible combinations for 10 card -king with the remaining suit combinations in the ones place.
They will occur 4 times per 10’s place value. There are 13 of those values 0-C. 13x4 = 52.
And that is it!
We have mapped our last 52, in a non sequential manner, but have mapped 96 percent of our system in a way we can use. Only having 52 Card specific images, with 300 images to explore other systems with!
And here are the card blocks a different way for you to copy, paste, print.
0 (also 44)
2 (also 84)
6 (also 48)
7 (also 88)
Phonetic Grids - Consonant, Consonant, Consonant
|Base 13||Base 10||Base 10|
|0 - (s/z)||0 - (s/z)||0 - (s/z)|
|1 - (t)||1 - (t)||1 - (t)|
|2 - (n)||2 - (n)||2 - (n)|
|3 - (m)||3 - (m)||3 - (m)|
|4 - ®||4 - ®||4 - ®|
|5 - (l)||5 - (l)||5 - (l)|
|6 - (sh/ch)||6 - (sh/ch)||6 - (sh/ch)|
|7 - (k)||7 - (k)||7 - (k)|
|8 - (f/v)||8 - (f/v)||8 - (f/v)|
|9 - (p/b)||9 - (p/b)||9 - (p/b)|
|A - (g)||(…KING)=omitt|
|B - (d)|
|C - (h)|
Phonetic Grids - Consonant, Vowel, Consonant
This is Katie Kermodes Phonetic System as I understand it. I believe she creates it by making 1 - t only and 7 - k only, and then reallocated d(formerly1) to B(queen) and g(formerly 7) to A(jack). H is added to complete the base 13 system as the start of the word. The sounds g, d and h only will occur at the start of a word.
J is used as a “sometime” situation. Where maybe it’s best to never use it, but when short on words for images, it may be used in both as 6 or 7, perhaps.
|Base 13||Base 10||Base 10|
|0 - (s/z)||0 - (oo)||0 - (s/z)|
|1 - (t)||1 - (a)||1 - (t)|
|2 - (n)||2 - (e)||2 - (n)|
|3 - (m)||3 - (i)||3 - (m)|
|4 - ®||4 - (o)||4 - ®|
|5 - (l)||5 - (u)||5 - (l)|
|6 - (sh/ch)||6 - (A)||6 - (sh/ch)|
|7 - (k)||7 - (E)||7 - (k)|
|8 - (f/v)||8 - (I)||8 - (f/v)|
|9 - (p/b)||9 - (O)||9 - (p/b)|
|A - (g)||(…KING)=omitt|
|B - (d)|
|C - (h)|
Let me know if you need clarification. If you had thoughts or feedback please let me know. I’m about to invest some considerable time into this system.