## Fermilab’s Strange Letter

Note to readers: I’ve got some very interesting progress up here.

There’s a great post over at symmetry magazine about a strange letter they received a year ago, written entirely in some sort of code. The actual letter can be seen here.

Looks to be rather interesting. At first grasp, we can see that the top “paragraph” seems to be in some sort of base-3 notation (either 1, 2, or 3 lines in a group), and the bottom paragraph in a similar manner seems to be in base-2.

The middle section seems to correspond somewhat with hexadecimal digits, and there are three letters from the code above the “last” paragraph. If we take it to be a partial code, it spells out “SFC” – the only SFC I could find in relation to Fermilab (who publish symmetry magazine) was the quasi-related Societe Francaise de Chimie. I’m thinking dead end, anyone else have any other bright ideas?

Rough work follows:

Top paragraph, grouped by line:
(3,2,3,2,3,3,3,3,1,1,1,2,1,3,2) (15 total groupings)
(3,3,3,2,3,1,3,2,2,1,2,3,3,1) (14 total groupings)
(2,1,1,1,3,3,1,1,3,2,3,1,2,2,3,3) (16 total groupings)
(3,3,3,2,1,2,1,2,3,2,1,3,1,1,3) (15 total groupings)
(3,1,1,3,3,3,3,1,3,3,3,1,1,1,1) (15 total groupings)
(2,1,1,3,3,3,3,2,3,2,3,2,2,1,1) (15 total groupings)
(2,3,2,3,1,3,3,3,1,1,2,1,2,3,1) (15 total groupings)
(3,3,2,3,1,3,1,2) (8 total groupings)

Top paragraph thoughts: total number of groupings, 113. 113 is a prime number, this may be significant. Is there any significance to the fact that the numbers on the second and third lines are 14 and 16 instead of 15 and 15? In decimal notation this would be 720113244210716512990341782103795379056660114385796527.

Middle paragraph, grouped by line, hex only:
(F,0,B,E,5,8,F,2,F,D,6,3) (12 symbols/hex digits)
(6,C,7,9,D,2,E,4,9,3,E,6) (12 symbols/hex digits)

Middle paragraph thoughts: Why are there symbols at all? This appears to be information duplicated in two codings. Hex digit frequency (digit-freq): 0-1, 1-0, 2-2, 3-2, 4-1, 5-1, 6-3, 7-1, 8-1, 9-2, A-0, B-1, C-1, D-2, E-3, F-3. In decimal notation this would be 74506518313470710988407084006.

Random line: S (unknown symbol?), F, C. Why is there a symbol there, directly after definition of symbols, that is not defined? Is it the undefined hex digit A? Is it significant that the “beginning” is defined?

Bottom paragraph, grouped by line:
(1,1,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,1,1,2,1,2,1,1,2,1) (36 groupings)
(1,1,2,1,1,2,1,1,2,1,2,1,1,1,2,1,2,1,1,2,1,1,1,2,1,2,1,1,2,1,1,1,2,1,1,1,1) (37 groupings)
(1,1,1,1,2,1,2,1,2,1,1,2,1,1,2,1,2,1,1,1,2,1,2,1,2,1,2,1,1,1,2,1,1,1,2,1,1) (37 groupings)
(2,1,1,1,2,1,2,1,1,2,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2) (37 groupings)
(1,1,1,2,1,1,2,1,1,1,2,1,1,1,2,1,2,1,1,2,1,1,1,2,1,2,2,2,1,1,1,2,1,2,1,1) (36 groupings)
(1,2,1,2,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,1,1) (37 groupings)
(2,1,1,2,1,1,2,1,1,1,2,1,1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,2,1,1,1,2,1,2) (36 groupings)
(1,1,2,1,2,1,2,1,1) (9 groupings)

Bottom paragraph thoughts: 265 total groupings, prime factors are 5 and 53. In line 4, 2111 repeats 6 times, the square root of the number of groupings in the first line. 1 occurs 179 times (prime number), 2 occurs 86 times (prime factors 2 and 43). 2 never occurs more than once, and 1 occurs either as 1, 11, or 111. In decimal notation this would be 4785997412726154595979555835418260996622867313584208882680343839351760783444564.

Assuming “II” is a seperator, the last “paragraph” reads:

(3,1,2,1,1,1,1,2,1,1,1,3,1,2,1) (15 numbers)
(2,2,2,1,3,1,2,3,1,2,3,4) (12 numbers) (4 at end)
(4,1,1,2,2,1,3,1,1,1,3,3,2) (13 numbers) (4 at beginning)
(3,1,2,2,3,3,3,3,3,3) (10 numbers) (long streak of 3s)
(3,2,3,3,1,2,3,1,3,1,2) (11 numbers) (multiple “II”s after each other)
(1,1,2,3,3,3,2,3,1,1,3,3) (12 numbers)
(2,2,3,2,3,2,3,1,2,3,1) (11 numbers)
(2,1,1,2) (4 numbers)

88 total numbers, prime factors (2*2*2*11). New problems: the 4s. We haven’t seen this before. Also, if 2 is a seperator, why does it separate nothing near the end of line 5? I’m not sure if this is the correct approach.

#### Geoff

lives and works in Ontario, Canada.

### 17 Responses to “Fermilab’s Strange Letter”

1. When I read the ‘S” I thought perhaps it was Sincerely (F)(C)… but this seems less likely the more I look at the code. The 3 character grouping seems to be quite significant to me.

2. Ok. check this one out – found something related to fermilab S (F)(C) = Shoemaker F.C.
http://usparc.ihep.su/spires/find/hep/www?rawcmd=a+Shoemaker,+F+C

Something to do with Muon-Nucleon Scattering Proposal PDF link to proposal here:

http://lss.fnal.gov/archive/test-proposal/0000/fermilab-proposal-0307.pdf

going to go read this now…

3. I think the shoemaker guy’s a dead end… that paper I read was published in 1974 and I can’t find anything else about him on princeton’s site or anywhere else…

4. You counted “F,2″ in the middle paragraph twice. So both lines should be 12 symbols/digits.

5. Indentation counts. Five trinary numbers, (middle part), five binary numers. The lengths seem to match up: 29/46/14/14/8 vs 73/110/37/36/8. I suspect the key to the puzzle is determining how to reconcile the binary and trinary versions of the message.

Check out my post at http://it.slashdot.org/comments.pl?sid=555280&cid=23437390 and yes, 75, should be 73.

6. More context (credit jhan via /.)

The top and bottom part of the code code the same data. The little indentation at the beginning of the line is important and means that the previous line continues. The indentation in the bottom bottom part is of, perhaps because of writing conditions. The top part consists of five trinary numbers of lengths 29, 46, 14, 14, 8 digits. The bottom part consists of five binary numbers of lengths 75 (ed: should read 73), 110, 37, 36, 8 digits. My best transcription, probably with errors:

``` char trinary[8][40]={ "323233331112132", // 15 "33323132212331", // 14 29 "2111331132312233", // 16 "333212123213113", // 15 "311333313331111", // 15 46 "211333323232211", // 14 14 "232313331121231", // 14 14 "33231312"}; // 8 8 char binary[8][40]={ "111010110101010101101010101110101101", // 36 "1101101101011101011011101011011101111", // 37 75 (ed: 73) "1111010101101101011101010101110111011", // 37 "0111010110110111011101110111011101110", // 37 "111011011101110101101110100011101011", // 36 110 // Should have been more clearly to the left? "1010110111011101110110111010101110111", // 37 37 // Should have been two steps to the left? "011011011101101110110111010110111010", // 36 "110101011"};```

7. I disagree about the “binary” portion having five numbers. I see three numbers. They are rows 1/2, 3/4/5, and 6/7/8.

8. Sneaky. The “indentation” is whitespace. Remove linebreaks and end up with this grouping.

323 233 331 112 132 … 1
333 231 322 123 312 … 2
111 331 132 312 233 … 3
333 212 123 213 113 … 4
311 333 313 331(111 … 5 113
2) … 6 (this is really 113 after bringing the leading II mark to join the I mark on previous line)
113 333 232 322(11 … 6 133
23) … 7 (this is really 133, I III III after bringing the II III to join previous line)
231 333 112 123 133 … 7
231 312 … 8

Make this base-3 and you get

212 122 220 001 021 222 120 211 012 201
000 220 021 201 122 222 101 012 102 002
200 222 202 220 002 002 222 121 211 022
120 222 001 012 022 120 201

where 000 = a, 001 = b, and so on …

Then do substitution cipher …

9. The first part can be decoded as “frank shoemaker would call this noise”.

Interpret ‘I’ as 1, ‘II’ as 2, ans ‘III’ as 0. The resulting trinary numbers are mapped to 000=’ ‘ (space, 001=’a', …etc This results in “frank shoemaker would camv ftvtcapsbc”. Some minor corrections to the input results in the final string.

It seems that Shoemaker is not a dead end.

10. Using a base 3 code, let
000=space
001=a
002=b
010=c

220=x
221=y
222=z

If |||=0, |=1, ||=2, then the first section can be rewritten as:
020 200 001 112 102 000 201 022 120 012 111 001 102 012 200 000 212 120 210 110 011 000 010 001 211 211 000 202 022 100 201 000 112 120 100 201 012
(errata: the line break at the end of line 6 has broken a symbol in two, and one of the symbols in line five is wrong)
“Frank Shoemaker would call this noise”.

In the last section, the double bar is a gap between symbols as suggested above. Again, |||=0, |=1, and ||=2. The last section can be rewritten as:
012 111 121 110 120 221 012 012 000 112 210 111 002 012 200 000 002 001 201 201 012 000 201 100 220 202 012 012 112
(errata: the line break at the end of line 2 has broken a symbol in two, and there is a duplication of a whole triad in line 5)
“employee number base sixteen”

Perhaps the three symbols before the last section is the employee number of the author (S252 in base 16). Or perhaps ‘s’ encodes to either 1 (or less likely A), in which case the employee number would be 508. Or maybe just “S F C” for “Shoemaker, F C” as earlier suggested.

Not sure about the middle section (apart from it acting as a decoder for the employee number).

11. [...] now we’re getting somewhere with the strange letter Fermilab received. Looking at the top paragraph first, with I=1 II=2 and III=0 we [...]

12. the hex code seems to define everything one, two or three times but simply replacing each number with the number of times its defined and then decoding gave me gibberish (ddft/dzer, im known for my frequent rather stupid errors, so someone may want to double check this) but since the other two sections both rely on this key it may be more than cooincidence.

13. I also attempted to decode based on the number of times a symbol was defined, and also got gibberish. Although my method was different. “0″ is also undefined in the letter, could S simply be 0? If that’s the case, then the employee number is just 252. Anyone know who that is, if they exist?

14. Oh, I’m stupid, “0″ is “i”, my bad.

15. [...] (creator of the Homebrew Air Conditioner and employee of the Canadian Space Agency) noted that the first and last paragraphs appeared to be in base-3 and base-2, and got to work. By the 17th, he had experimented with possible mappings and reached a solution. [...]

16. I think we have to consider the possibility that the “Frank Shoemaker” decoding is a deliberately planted red herring. It’s way too easy, or to put it another way, the apparatus of the base-3 and base-2 coding is out of place, given the ridiculous simplicity of the cipher.

Furthermore, the implication is that something which passes for noise here is NOT in fact noise. For example, is “BASSE” truly just a typo? C’mon. If so, this isn’t really a very sophisticated or interesting exercise.

I’m guessing there is another message hidden beneath or within the portions that have already been decoded.