Speculative fraud hypothesis

[Jorge_Stolfi]

One thing which could be interesting to do is to compare the copy&modify algorithm with a version of it without the copy&modify part, but with the same generation rules. The idea is to generate one word at time, always starting from a null string and applying the rules a random number of times (a few times) for each generated word.

I will let others do that for Voynichese, with the T&T Mutate procedure.  Meanwhile, just for fun, here are the results for English, using my "English-tuned" Mutate procedure.

Again, my Mutate procedure randomly chooses between "insert", "delete", and "replace, with probs proportional to the total frequency in an English corpus of words whose length is greater than, less than, or equal to the length of the given word.  The procedure then scans the word collecting the possible interventions of that type, and the merit of the result of each intervention.  Specifically:

• For "insert", each candidate is a pair of consecutive letters XZ in the word and a letter Y, and the merit is the count of occurrences of the trigram XYZ in the corpus.
  
• For "delete", each candidate is a triplet of consecutive letters XYZ in the word, and the merit is the count of occurrences of the digram "XZ" in the corpus.
  
• For "replace", each candidate is a triplet of consecutive letters XYZ in the word, a letter W distinct from Y, and the merit is the count of occurrences of the trigram "XWZ" in the corpus.
  

Then the procedure chooses one candidate intervention with probability proportional to its merit, and executes it.  The digrams and trigrams include start-of-word and end-of-word, so the three operations above may be applied to the first and last letter as well as internal letters.

The corpus is the full text of Well's novel War of the Worlds ("WoW"). 

The simulation starts with the word "phleghm" (which is not in the corpus), applies the Mutate procedure above M times, and outputs the result.  This is repeated 10'000 times, independently.

Results [Note: the curve labeled "T&T" in the Zipf plots is actually for my Mutate applied M times]:

M = 1

  pheghm phieghm pheghm phlegthm hleghm phleghmy hleghm paleghm
  phlleghm phleg-m pheghm pheghm hleghm pheghm phlegh hleghm
  phlighm phlegham pheghm phleghe pleghm pheghm pheghm pheleghm
  pheghm pheghm phledghm phlethm phieghm pheghm pheghm pheghm
  hleghm phreghm pheghm hleghm pheleghm phleghme phlleghm
  phlerhm pheghm pheghm pheghm phleghme phlerghm pthleghm pheghm
  phleghe hleghm hleghm ... hleghm phlegthm pheghm phlegh pheghm
  pheghm pheghm hleghm pheleghm phleghe pthleghm pheghm pheghm
  hleghm uphleghm phlighm pheghm pheghm poleghm pheghm phlegh
  hleghm pheghm pheghm hleghm pheghm phlethm pheghm pheghm
  hleghm phlighm puleghm pheghm pheghm pheghm pheghm phlerhm
  hleghm pheghm pheghm phlegh phlegham pheghm pheghm phlerhm
  hleghm pheghm phlegh pheghm phleg-m

   
94 word types, 0 valid tokens, 10000 invalid

M = 2 

  phaghm phegthm hleghmy sleghm phllegh heghm pheghe hlegh
  phligham pheghe plegh pheeghm phenghm phledshm pheghm pherhm
  pieghm phreghm pheghe hlerghm phegh pheghmy phegh phegh leghm
  pheghe theghm heghm heghm pherghm heghm ptheghm peghm heghm
  hlighm phleghm phleth theghm phegh spheghm peghm phoeghm phegh
  hleg-m heghm phtegh phegthm pheghme pheghe phighm ... phegh
  heghm heghm heghm heghm phreghm phlegth theghm pthlegh hlenghm
  phligh phegh ptheghm hleghe phegh phlech heghm phlengh puleghe
  haleghm hleghim peghm heghm phegh leghm thlveghm heghm peghm
  heghm pheghm thleghm pherhm hlegh phegh leghm phleth pheghmp
  heghm heghm pheghm heghm phighm heghm phegh sleghm phegthm
  peghm uleghm hlighm upheghm

   
760 word types, 0 valid tokens, 10000 invalid

M = 3

  haghm hlegthmy sledghm heg-m hegh hlighem heghe preghm
  phenighm phethm pherm pellegh phegthe hegh pheghm pheg leghe
  deghm henghm pheeighm heghim hegh hethm heaghm phlet paleg
  sphegh pedghm pheth eghm phegh phenghme pheghed hegh pegthm
  hethm philenh shegh pheg peghe popleghm theghe herghm phlug
  herhm theghme pheghe lethm pegh eghm ... peghum hegh eghm
  phlnegh ptherghm alleghm hlvegh hligh pheghm hegthm hedghm
  hegh ptheg-m thlighe paletchm eghm hegh phugh pegam phighe
  hehm highm eghm hlleghm phegh hlexhmy eghm pheighm scheghm
  pthegh pechm theghm hegom haghm phigthm hegh eghm hlethe
  theghm thleg-m threghm poughm hegum deghm eghm hregum phlext
  eghm heg-m eghm

   
1848 word types, 0 valid tokens, 10000 invalid

M = 4 

  hagham haghmy hlegh hegh phighas poleg phenithm pethm pinghm
  hegthe heght hesh pegh ethm hugh highim hregh herm heilegh
  thoghm pegh heth egh hlithm pheghe hugh thaghm theg heghm phed
  pheght theg hethmy hugh theghmbe ligh teghem hegthe thethm
  pherthm whegh hengthm heg-sm pheghe leghe poleeg peam wthlegh
  theghmy hehe ... pigh slege-m eg-m hethm hege pegn peg hunghm
  hegth hegh hehe plegh egh hlege thineghm heh hegho phe heg teghm
  thegh heghe heghe peeg-m hlitim heg eg-m hilewh heghe hltegh
  hegh pehe hetchm polegat lerh pthegh hlseth pole ceg-m hlegte
  hehm ptenghm heghm upheg upegh eneghm beghe tiegh htogh heram

   
3031 word types, 121 valid tokens, 9879 invalid
 
M = 5

  agham henghmy peg hligre pole phathm ther egthe hegh thug aghm
  hecanghm heghim eng-m phlet palar pregh hesh legthm pheghed
  hughe mengh beghe phe peght thee hegh alighmbe cigh hegeam
  thethe heghth hegh pe-gtum hlegher pheghe poleege pegs ileghmy
  pegum enghim haigh ege thethe lighm yeg eghm egh hllegt
  ptchega ... eathm eghme tllehim alegs hedghe pengh hedsam
  hic-m hug lewh hedg pthweghe hlere hethm heghm phers legh
  herkm mehm heckhm peghm theght hm sphedg egh peigh olergh
  peshm igh hegh hig tethe tchigh peg heredgh opughim wegh haghe
  hregs hegh phige g-m egre phege heghmy edg-m lege plege heck eghm

   
4179 word types, 227 valid tokens, 9773 invalid
 
M = 6

  aghamy edg-m ery higs aghe tcher hegh hesh pach einghm ighim
  ng-m hreixegh alag hed leghm ptaghe erch prrhmy thleghle heghe
  terthms hut eche tegeam tethe herhm tengthm heg-sit peghe
  polege wthegs theghe ham ough ere theigre bene-m ghe eckhe
  hleate hege hugh hathm eg-m er-m heg aghi gers ig ... perim
  lerwhem eghe hle enum cleg hug-m eerm negme hegum eg ileg ere
  thm upeghe high gh-m hegth knegthm pere-m ber pegts egthm egre
  ig-im hatege bedg heghe aleg-m fleem heedshe ptath let aleg
  thush hegth lplegh pewh acth hlueghe sple pege thegle ejedgh
  h-ghm exhi eig egim there hethe

   
5165 word types, 377 valid tokens, 9623 invalid

M = 20

  wait ionedem whenct tesp rilved arioud foui cohee t'se ovoie-e
  idin ne sph tur dun iffs lane ar asthe ale sabor tht scarn
  ache at setes sued shon whined asppt ree swen en end an te
  tiom amale bumm peong hrof the seme rine pevely feea plin juf
  ablee asei ... nif mang ive mend aber grche thim isiay brelle
  ebrhin ofire thagly yged mard hapan gr soo nifth whe menth
  ievem lige tery agro mbe ime wik sthe ullft as aght head its
  gond hup aye unses upil trre lper men sad gre tht edge bysie
  fes ache tcht elll

   
6940 word types, 995 valid tokens, 9005 invalid