# A new 10-digit binary system

Hello world,

For those here who do not know me, my name is Lance, and I’m an American MA. One thing I enjoy is building or more often merely contemplating complex systems. Just the fact that a system can be complex, useful, and ultimately understood is intellectually stimulating in its realization, and the creation of such a system is intellectually fulfilling, especially when a system is brought about by altering standard rules in a new and creative way that had so far been unforeseen. An excellent example is what Ben did with the major system. Another example is what Hannes did with the fundamental 2-card principle of the Ben System, and a third example is a 2-card system that I have developed out of Hannes’ ideas, and Ben’s by proxy I guess you could say.

You can search for the shadow system and read my thread about how I decided to set up the phonetics for a 2 card system with only 1352 images (following in Hannes’ footsteps as far as using only 1352 card pairs). This ten digit binary system is built for the user of the shadow system. The shadow system is built in such a way that the 1352 can be expanded to a full 2704 system, which is what I have done myself, though it is not at all necessary.

The advantage of a 10-digit binary system over all others is that for every locus that is forgotten, all three images in a single locus even, 30 points are deducted from the overall score. This is not so important in 5 minute binary, where we strive to get everything correct. But in 30 minute binary, Ben, the long time world record holder, doesn’t care if he gets them all right. To be more precise, he doesn’t even try. Why should he, when he can encode so many digits that the errors along the way add up to a minimal penalty overall. I believe in theory that the 3x3 method of binary is the best for speed if a person can learn to see all 512 images as shapes. It will be faster. In 30 minute binary however, placing 10 images across 3 rows means if any 1 of those ten images is forgotten, up to 90 points can be deducted. It’s fast, but you had better not mess up often or it will be a great detriment to your score.

The Ben System is big. It’s extremely ambitious. It’s hard to make, hard to learn, and requires maintenance. It’s great. But not everyone wants to do it.

He starts with a consonant for each of the 16 possible suit pairs, then a vowel for the first card, and a final consonant for the second.

In a 4-3-3 binary pattern, there are 16 possible beginnings:

0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

Each of these could be assigned the 16 suit pairs’ consonants. Then the 3-3 after that will be the vowel and consonant of the first and second card, and so there is a 100% overlap in images. But to build those 1024 in that fashion without carrying the full Ben System would be wasteful in my opinion. It wouldn’t even give you a 3-digit system to use, nor a full 2-card system, nor even a 1352 2-card system as far as I can tell, though there may be a way around that latter statement. I don’t care to give it any thought because I will not be doing it myself, but that’s just food for thought, neither here nor there.

My 10-digit binary formulation does require images over and above the original 1352. But only perhaps 8 or 16 new images. I’m not completely sure how many because I didn’t fill those images out yet and I’m not concerned to answer the question now. Though the answer may naturally arise by the end of this post.

More soon.

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In the original Shadow System post, I described the rules for a theoretical 10-digit binary system in the form of
1-3-3-3 or 0-3-3-3. If the first digit was 0, you would use the original image. If the first digit was a 1, you would use the shadow image.

To use it, you would have to build the full 2704 shadow system, so it scores no points over the Ben System in that respect. The reading of the 1’s and 0’s is so hard to get out of your mind that for as long as I practiced it, which wasn’t very long I admit, I couldn’t help but read 4 chunks of information instead of 3. In short, it was vastly inferior to Ben’s formulation. It was worth a shot I suppose. I thus resigned to the use of the 3x3 matrix system, which I quite like, and yet, the disadvantages it would have compared to Ben’s 10-digit formulation in 30 minute binary, which is the only binary event at the WMC, kept me wishing there was some way to devise a 10-digit system with only the 1352 required objects to use the initial phase of the Shadow System, which works very well on its own and is far easier to complete.

So the other day, I worked it out. On the expert level, a sound argument could be made that my 10-digit formulation is inferior to Ben’s formulation, but by very little. With the time you save by not building a 2704 image system, you could very easily catch up and surpass Ben System users. But in the long run, Ben’s wins out. However, the gap in efficiency between these two formulations is, I believe, considerably smaller than the gap in efficiency between a 1352 and a 2704 system. And that gap, while notable, is certainly not so great that the construction of a 1352 image card system should be written off. In short, these 10-digit systems are close.

Explanation soon.

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The advantage of Ben’s 10-digit binary is that there is a perfect consistency in how the digits are read. In mine, there are new rules to be learned.

Let’s start with the first 8 out of 16 groups of 64 images each.

0000 - 0
0001 - 1
0010 - 2
0011 - 3
0100 - 4
0101 - 5
0110 - 6
0111 - 7

Examples:

0000 001 010 - Sudden (012)
0001 001 010 - Titan (112)
0010 001 010 - Newton (212)
0011 001 010 - Maiden (312)
0100 001 010 - Rotten (412)
0101 001 010 - Olden (512)
0110 001 010 - Judean (612)
0111 001 010 - Cotton (712)

Simply put, the first 0 is not relevant in the sense that you just ignore it and carry on with the major system as usual. After this point, we drop the conventional reading of binary digits, because almost no one can naturally read binary digits beyond the numeral “9” anyway. So we’ll take what liberties we need to make the method easiest for us.

Now we move on to:

1011 - 8
1101 - 9

Notice the first 3 of those four digits. It will be helpful in explaining the naturalness of the selections of combinations of 4 binaries to represent certain sounds.

Examples:

1011 001 010 - Futon (812)
1101 001 010 - Button (912)

Now I am assuming that this is for the user of the particular 1352 system that I have laid out. In that case, he will be using Kings to make the ‘H’ sound when they appear first, and to be silent when they appear second. In the latter case, the card pairs can be read merely by seeing the second king and ignoring it.*

Kings first: 1001
Kings second: 1111*

Examples: (Let us assume that the suit combination = 1 in your system)

1001 001 010 - Hidden (K♠2♣)
1111 001 010 - Ton* (2♠K♣)*

Thus, we have the first example of the new idea introduced in this 10-digit binary method. That the first four digits can usefully index the correct image without making a sound themselves. And it is this rule that is employed for the final four groups of images.

1010 - Delayed 8
1100 - Delayed 9

Notice the resemblance to the natural ‘8’ and ‘9’ listed above. Hence, the difficulty of learning these 2 codes is minimized.

Examples:

1010 001 010 - Donovan (128)
1100 001 010 - TenPins (129)

At this point, we have covered 14 of the 16 categories needed. Here are the final two:

1110 - Delayed Jack
1000 - Delayed Queen

As in the shadow system, the rules when a Jack or a queen appears second in the card combination is that an “S” is added to the beginning of the word. Queens make the “4” sound, so 1000 is quite a fitting combination for them. 1110 has nothing to do with Jacks really, so just has to be learned through repetition.

Examples:

1110 001 010 - Stand (2♠J♣)
1000 001 010 - Stoner (2♠Q♣)

Thus, 1110 and 1000 both make the sound of “S” while indicating which word must be used upon the reading of the next 6 binary digits.

And there you have it: a complete 10-digit binary system for users of a 1352-image card pair system.

Questions are welcome

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Lance, this is brilliant!

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Thank you May of 2014. Wow.

I’ve worked on and with plenty of 10 digit binary formulations at this point, and I can only recommend any of them to someone who plans on memorizing without review and capitalizing on the low error-penalty. 3x3 is just going to be faster. You could get a lot of mileage out of it in 30 minute binaries potentially, so if you mostly care about 30m-bin, it may be worth a try.

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I started to finally see some progress with 3x3 after lots of practice. Now that I have experience with that, I am going to try this 4-3-3 for a bit and see how it goes. It might be better suited for 30 min binary, but if I go a touch slower, which can help with precision, I can possibly avoid having to do any review in 5 min binary and end up with a respectable score still. To be continued…

I might also switch the Kings First and Delayed Jack codes.

Delayed Queen is 1000 which is intuitive, so having Jacks as 1001 makes sense to me.
Kings 2nd is 1111, so having Kings 1st as 1110 also makes more sense I think.

Any reason you can think of not to do this?

It would look like this for me:

1000 - Delayed Queen (intuitive because, as Lance said, 100 = R which is what Queen is)
1001 - Delayed Jack (1 value removed from Queen, plus the delayed Jack makes a “T,D” sound, which in binary = 001, so this is a more natural fit I think)

1010 = Delayed 8
1011 = 8
1100 = Delayed 9
1101 = 9
1110 = Kings 1st (better for me since it is 1 off of the other Kings value)
1111 = Kings 2nd

I found an issue with this and will need to make additional images for my system. And here I thought the 1360 I made for the Shadow System would be enough!

Based on the phonetics above, these require custom images as there are no suit combinations for cards that spell out ‘4’ or ‘R’ (100 in binary):

Delayed Queen:

1. 1000 100 000
2. 1000 100 001
3. 1000 100 010
4. 1000 100 011
5. 1000 100 100
6. 1000 100 101
7. 1000 100 110
8. 1000 100 111

Delayed Jack:

1. 1001 100 000
2. 1001 100 001
3. 1001 100 010
4. 1001 100 011
5. 1001 100 100
6. 1001 100 101
7. 1001 100 110
8. 1001 100 111

Kings 1st:

1110 100 100

Kings 2nd:

1111 100 100

If you don’t use the SS or are not familiar with it, this may not make much sense.

For the 5 Minute Dates event, for the 2000-2099 years, I use my Kings 2nd images as they are 2 syllables and match up perfectly for this purpose. I just had to custom create images for 2044,2048,2084,2088. Now I get to make another 18 images! Well 17 I guess since the image for 1111 100 100 = 44 and I have an image for that already which is my 2044 date.

In total I will have 1381 images now to account for numbers, cards, binary, and dates perfectly.