# Tables of Soyga: the primary mobile automaton? Anders Sandberg

*by*Phil Tadros

### Tables of Soyga: the primary mobile automaton?

Was the primary mobile automaton supposed to do encryption and/or summon angels?

Usually the historical past of cellular automata begins with von Neumann’s classical study of self-replicating systems in the 1950s. Whereas clearly influenced by Turing’s discrete automata, this was the primary paper utilizing a grid of cells in numerous states the place every cell modified every clock tick in keeping with a hard and fast, common rule. Even Stephen Wolfram seems to think so: “Regardless of their quite simple building, nothing like common mobile automata seem to have been thought-about earlier than in regards to the Nineteen Fifties.”

However perhaps von Neumann was scooped by a couple of centuries.

## Liber Soyga

*Liber Soyga* is a early fashionable guide. It was owned by Dr John Dee, the Elizabethan scholar, magician and authorities adviser (try Leslie A. Rutledge’s entertaining “John Dee: Consultant to Queen Elizabeth I“). He talked about it in a couple of areas, however the identification of the work was misplaced for a few years. In 1994 Deborah Harkness managed some good scholarly sleuthing and located copies on the Oxford Bodleian Library and the British Library (filed beneath an alternate, non-obvious title).The work accommodates varied items of astrology, cabalism, lists of supernatural names and summoning formulation. On the finish there are 36 36×36 squares of apparently random letters, labelled by the constellations (twice), planets, parts and the phrase “magistri”.

An instance is the primary sq. of Aries:

ndizbdizbdizbdizbdizbdizbdizbdizbdiz

isrlytrlytrlytrlytrlytrlytrlytrlytrl

scucbxibaxibaxibaxibaxibaxibaxibaxib

roernmhggdokqsrnplfdfzlyqsrnplfdfzly

aqbtxdnxytybscuefnutohqtauiducisohqt

mppimcqsgbadzelbhsekfkhaczlaysrfqegb

mozlirdziqxthkceykubhpxqzbnpmreuhkyr

aqucmqablnmsqgitgqrnygdxppcsuiteybat

rdbectiqhsukhmhaigzpmffzrcfumhageqxl

smagikasqpkbkdnpyypeciupgiumlepuuhco

icdmhpoctzmamcqmxozgizygnzydqbrhbksy

nrpbkgusdecdroaofquyabaidensadyzdphd

nhurxymrpslatyqlctenpporpsxkqaabfrtm

iymqsgsbrfnpingrodkefrbtzunasipptbxd

sgsauykreueflkyiessnuiqqummzuarcyris

rscdbamqbyuxcnnzgauelfsaydrlrmqzatrf

ausmacpfddbzedshmzyuciipmcucudxpodyx

mtcpolmesmabgkkzohdbezlmlzysesfrbfaz

mslmnbonicdgnamyfktkupaothdzgahyrrmy

aucpceedolaidfogmikbygguleshmzkobtuo

rhhusntmnbcmciexdoskopumkukzohpdgbyf

sqelpcydsksusrqsmniaqmtubybbqeffiqto

iglhusgkkbumregaoxactulrnnqyhkxxasdt

nxclrfiamaydyuyqlsirgcobpctgosfzcxtd

nmbnhlfcpogkoengrflopqlygikyfuxpqsdi

icednbhhufiaqbpuiucrcttgnzmxxmugyktr

slbfppxzyxactkgcmtlolqqdshrimlrsgqqo

ryrrcsfbazcfxbirzxcryhxtclorznhzigyf

aatbeiurmysofdobbzehdnmslhtbbpxpyyoo

mzxrqfyicbufhieqypsqapbuclqyrcarkoyf

mynhxxorokmeyagyozuhfrnlzngehhftsyoo

aapxnmnhtsuuoixoypkzhyebbpuuzkxlpmne

rmofpbpxlpkmnzzqtzmyzaghgxmthplhudsn

sufhurcanfmlkpngbbogfckzimlqefnymcxe

ilclrermmecoszpurnexxsshouctnuencfzg

nbebtnhrzgieiozyidknmrfkfysdsetxsohm

That is just like many different early fashionable magical books: John Dee is himself well-known amongst hermeticists for his “Enochian squares“. Precisely how the Soyga squares have been for use is seemingly unclear; Dee himself tried asking the archangel Uriel if the guide was any good however acquired informed that it was above his clearance.

The following step of the story is that the Soyga squares were reverse engineered by Jim Reeds. He discovered the rule to generate them: a key phrase is used to seed the left edge (the phrase is written downwards, adopted by itself in reverse, in the correct order, reverse, and so forth – within the above instance the phrase is “nisram”). Every cell is determined by the cell to the left and above itself: the letter to the left determines what number of steps ahead within the alphabet to maneuver from the letter above.

L(i,j)= [L(i-1,j)+f(L(i,j-1))] mod 23, if L(i,j) is the letter in row i and column j. f() is an apparently arbitrary record of values. The highest row is generated by L(1,j)= [L(1,j-1)+f(L(1,j-1))] mod 23, taking the left letter as the highest letter too.

Plotting the outcome as coloration slightly than letters provides the next sample:

## The Soyga Automaton

The cool factor is that that is basically a 23 state 1D mobile automaton, the place the time is working from the left to the correct.The dynamics is strongly chaotic (class 3), producing an apparently random distribution of letters. There’s a slight bias due to the highest boundary situation: there are two attractor states alongside the highest, one consisting of repetitions of ”dizb” and considered one of repetitions of “oy”. The oy attractor tends to provide a triangle of repeated “oy”. However even when the key phrase is simply “a” the sample is chaotic (as demonstrated within the picture on the high).

Utilizing this sort of rule generically produces pseudorandom habits: practically any transition desk f() will work. Some have triangle slices alongside the highest of repeating patterns, however most appear to strategy a good distribution of letter frequency.

That the dynamics is generically random for many-state automata is well known.

It’s much less apparent that it could additionally generate a good distribution of states. Nevertheless, if one seems on the transition desk T(i,j) denoting what letter one will get from having letters i and j to the left and above the uniformity turns into extra apparent: every row is a round shift of the alphabet, so the whole variety of situations of every ensuing letter is identical. A random transition matrix would have produced some letters extra typically than others. There may be nonetheless the problem that some matrices like these might need subsets of letters permuted to one another (think about one the place even letters are became even letters and odd ones into odd), so some key phrases would induce an uneven distribution. However presumably ergodicity is generic for this class of automata.

## What was it good for?

Why did the originator invent this rule? Reeds compares it to different letter tables from the identical period, and it’s fairly clear that Soyga is certainly much more superior than the opposite tables. Most have quite simple repeating or zigzagging patterns. Rutledge notes that a few of Dee’s tables had crudely random patterns harking back to an individual filling them in by hand in an arbitrary approach.Most of those tables have been supposed for magical use: to make talismans or discover sacred names with the intention to carry out magical invocations of angels.

Nevertheless, I ponder if the aim was cryptographic: the medieval and early fashionable ciphers made use of tables of rectification. Trithemius *Steganographia* is talked about in Soyga, and is itself an obvious treatise on magic that really does include cryptographic work.

Hiding a cipher key within the type of a magical desk would appear pretty rational as a canopy at present, however given how far more delicate magic was again then (it landed each Trithemius and Dee in hassle) it’s a bit like utilizing unlawful pornography as a approach of hiding encryption keys: not precisely a discreet technique if any person pries.

Soyga might need been a technique of producing new tables that have been much more random than the Trithemius desk. It produces an uniform distribution of letters with practically no sample. Take the primary 23 rows and columns as a tabula recta and you’ve got one thing that might be much more immune to cryptoanalysis.

However provided that the Vigenère cipher was seen as uncrackable, was there a perceived want for anything? I believe that the urge to invent new encryption strategies has all the time been robust: if you have a cool idea based on your own field of expertise, you will suggest it (after all, if *you* cannot break it, it must be unbreakable!).

The truth is, using a change of the earlier column appears to be like an autokey cipher. The primary actual autokey cipher was urged ion 1556 by Cardano in *De Subtilitate*, however the first helpful on was invented in 1564 by Giovan Battista Bellaso. Vigenère printed one in 1586. Liber Soyga was talked about by Dee in 1583. May the Soyga automaton be the results of any person engaged on an autokey technique, maybe getting the intense concept of making use of it repeatedly to itself? It will appear to suit into the time.

In fact, the border between cryptography and angelic communication might need been blurry. Perhaps the tables have been seen as each: sufficiently superior cryptography is indistinguishable from magic.

Posted by Anders3 at April 17, 2014 12:06 PM