Ed Scheidts Mayan Symbols

 ▉ In this post I want to talk about a thing from the Kryptos universe that are not directly related to the statue.

▉ Mayan Symbols ▉

I think everyone who knows Kryptos knows Ed Scheidt. The former Chairman of the Cryptographic Center at the CIA and founder of the cryptosystems used around the Kryptos statue. As already shown in Part 4 of my Kryptos series, in the driveway of Ed Scheidts house, there are two symbols:

Figure 1 - Garage driveway of Ed Scheidt

We denote the left symbol set with $S_1$ and the right one with $S_2$. It took me a while to find his house on Google Maps - Street View. To save you some time, here is the link with a view on the driveway. I you go back in time in Streetview, you can see that the symbols were already there in 2012. But it is impossible to say when they were built. $S_1$ is clearly visible from the street, $S_2$ is hidden in the view. But you can use Maps (iOS) to see their positions (See Figure 2):

Figure 2 - Birds view of the driveway with marked positions of the two symbols

Ed himself explained during a Q&A session [4] at his home that these are Mayan symbols. The Mayan civilisation used a base 20 number system and the integers were not written from left to right but from bottom to top. Figure 1 shows the Mayan symbols and an example on the right side.

Figure 3 - Mayan numerals with example

To translate the Mayan symbols, you need to know where "bottom" is, as some symbols are ambiguous (i.e. $1,2,3,4,5,10,15$). For $S_1$, it appears that the symbols are aligned with the road so that a person walking along is in the correct position. $S_2$ seems to be $4$ separate integers, since they are written sideways, with the bottom also aligned with the road.

If you try to translate the symbols, you will notice that the third symbol in $S_1$ and $S_2$ (which is the same) is somehow wrong - it is upside down. I tried to find other sources of Mayan numbers that have some symbols reversed, but I couldn't find any. The number $9$ seems to be reversed. And that made me wonder - why the $9$ - or why the 3rd position? Did he made a mistake?

Why would we care about these symbols? I think if we could not even find the solution to this little puzzle, how could we solve K4? Below are some explanations, none of which are likely to be correct, but which may give you a starting point.

▉  Possible explanations ▉

1. House number and Postal Code

If you simply ignore that the third numeral is flipped and interpret the symbols from $S_1$ as (from bottom to top) $8,2,9,1$ you get the integer

$$\begin{equation} 1\cdot 20^3+9\cdot 20^2+2\cdot 20^1+8\cdot 20^0 = 11648 \end{equation}$$ But what is the meaning of $11648=2^7\cdot7\cdot13$?

Some people say that $S_1$ simply represents Ed's house number and $S_2$ the postal code. But his house number is $1048$ (as you can see in the Google Street view link). Ok, the last two digits are correct. However, the postal code is $22101$ which also do not match either symbols. Note that the correct base-20 representation of $1048$ is $$2\cdot 20^2 + 12\cdot 20^1 + 8\cdot 20^0 = 1048$$ Perhaps it is possible to find a logical way to translate $S_1$ to his house number that makes sense given the placement of $S_1$. But why should he write the postal code nearby his garage? And this does not explain why the symbol for $9$ is written upside-down.

Assume that $S_1$ represents $1048$, lets test what is in this case the value of the flipped symbol is

$$\begin{align*} 1\cdot 20^3+x\cdot 20^2+2\cdot 20^1+8\cdot 20^0 &= 1048\\ 8000+x\cdot 400 &= 1000\\ x &= -7000/400\\ x &= -17.5 \end{align*}$$ This does not make sense.

2. Date representation

The Maya used a slightly different method to represent dates. They did not use a strict base-20 system. Instead of $20^e$ for $e \geq 2$ they used $18\cdot 20^{e-1}$ for a better estimate of the $365$ days of a year (see [1] for details and [2] for a nice online date calculator). For example the date 03-11-1990 (D-M-Y) is written as

$$\begin{equation} 0.12.18.17.9.16 \end{equation}$$ which represents
$$\begin{equation} 12\cdot 18\cdot 20^3+18\cdot 18\cdot 20^2+17\cdot 18\cdot 20^1+9\cdot 20^1+16\cdot 20^0 = 1.863.916\;\mathsf{days} \end{equation}$$ The days are the elapsed days from the beginning of the Maya calender.

The symbol $S_2$ may be a date, since it is probably made up of $4$ separate integers. If we again simply ignore that the third symbol is flipped and enter $1,1,9,12$ into the date calculator, we get:

$$\begin{align} &0.0.1.1.9.12\;\hat{=}\;01.11.3093\;\text{BC}\\ \end{align}$$ which doesn't look interesting to me.

3. Ambiguity

We identified the third symbol as upside-down because we aligned the bottom of $S_1$ to the road. If we change top and bottom starting now with the $1$, then the fourth symbol is wrong, because the $1$ and $2$ stay the same when flipping them horizontally. So $S_1$ has some kind of ambiguity. We denote $S^\text{R}_1$ the symbol with bottom to the road and $S^\text{H}_1$ with bottom to the house. We get for $S^\text{H}_1$ (by ignoring the flipped symbol):

$$\begin{equation} S^\text{H}_1 = 8\cdot 20^3+2\cdot 20^2+9\cdot 20^1+1\cdot 20^0 = 64981 \end{equation}$$ Is it accidentally that
$$\begin{equation} S^\text{H}_1 \oplus S^\text{R}_1 = S^\text{H}_1 - S^\text{R}_1 \Leftrightarrow 64981\oplus 11648 = 64981-11648 = 53333 \end{equation}$$ ($\oplus$ means XOR)?

4. A hint towards Latin numerals

Somehow the flipped third symbol reminds me of Latin numerals. The first ten are:

$$\begin{align*} &1 = \text{I}\\ &2 = \text{II}\\ &3 = \text{III}\\ &4 = \text{IV}\\ &5 = \text{V}\\ &6 = \text{VI}\\ &7 = \text{VII}\\ &8 = \text{VIII}\\ &9 = \text{IX}\\ 1&0 = \text{X} \end{align*}$$ When being one step before a multiple of $5$ a subtraction is done, i.e., the $\text{I}$ comes first. So, should we interpret the flipped symbol as some kind of subtraction $5-4 = 1$? So replacing the $9$ with $1$ yields the number
$$\begin{equation} 1\cdot 20^3+1\cdot 20^2+2\cdot 20^1+8\cdot 20^0 = 8448 \end{equation}$$ , a palindrom number. I don't think this is correct but i am just guessing around.

5. Different basis

In the Q&A video I mentioned above, where Ed mentions the Mayan symbols in this driveway, he actually says [see [3] for details]:

… seeing the driveway that’s Mayan now it’s a two-dimensional Mayan it’s not a pictorial Mayan but there’s a code out there. Interesting…. Now there is simple substitution you know the Mayan language and you know how to handle base 60 then you’ve figured out the answer.

(Ed Scheidt 25-10-2015)

Mayan numerals are base-20, not base-60. Was this intentional or a mistake? Also, when I listen to the passage ([4] 25:40 min) in the video, I keep hearing "base sixteen". But even after playing around with different bases, nothing really made sense to me.

Perhaps the meaning is unknown to the rest of the world and the numbers have some kind of personal meaning to him.

So if anyone has another good idea i will add it to the list!

[1] https://maa.org/press/periodicals/convergence/when-a-number-system-loses-uniqueness-the-case-of-the-maya-the-mayan-number-system
[2] https://www.vinckensteiner.com/kultur/calendar/
[3] https://scienceblogs.de/klausis-krypto-kolumne/kryptos-workshop-transcript/
[4] https://www.youtube.com/watch?v=25YFYKKKkDo