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Xref: bloom-picayune.mit.edu rec.puzzles:18139 news.answers:3071 Newsgroups: rec.puzzles,news.answers Path: bloom-picayune.mit.edu!snorkelwacker.mit.edu!spool.mu.edu!uunet!questrel!chris From: uunet!questrel!chris (Chris Cole) Subject: rec.puzzles FAQ, part 4 of 15 Message-ID: <puzzles-faq-4_717034101@questrel.com> Followup-To: rec.puzzles Summary: This posting contains a list of Frequently Asked Questions (and their answers). It should be read by anyone who wishes to post to the rec.puzzles newsgroup. Sender: chris@questrel.com (Chris Cole) Reply-To: uunet!questrel!faql-comment Organization: Questrel, Inc. References: <puzzles-faq-1_717034101@questrel.com> Date: Mon, 21 Sep 1992 00:08:48 GMT Approved: news-answers-request@MIT.Edu Expires: Sat, 3 Apr 1993 00:08:21 GMT Lines: 1339 Archive-name: puzzles-faq/part04 Last-modified: 1992/09/20 Version: 3 ==> cryptology/Voynich.s <== The Voynich Manuscript is a manuscript that first surfaced in the court of Rudolf II (Holy Roman Emperor), who bought it for some large number of gold pieces (600?). Rudolf was interested in the occult, and the strange characters and bizarre illustrations suggested that it had some deep mystical/magical significance. After Rudolf's court broke up, the manuscript was sent to (if memory serves) Athanasius Kircher, with nobody on the list having been able to read it. It ended up in a chest of other manuscripts in the Villa Mondragone [?] in Italy, and was discovered there by Wilfred Voynich, a collector, in about 1910 or so. He took it to a linguist who wasn't a cryptanalyst, who identified it as a work by the 12th century monk Roger Bacon and produced extended bogus decryptions based on shorthand characters he saw in it. A great deal of effort by the best cryptanalysts in the country hasn't resulted in any breakthrough. William F. Friedman (arguably the best) thought it was written in an artificial language. I believe the manuscript is currently in the Beinecke Rare Book Collection at [Harvard?]. Mary D'Imperio's paper is scholarly and detailed, and provides an excellent starting point for anyone who is interested in the subject. David Kahn's "The Codebreakers" has enough detail to tell you if you're interested; it also has one or more plates showing the script and some illustrations. I believe D'Imperio's monograph has been reprinted by Aegean Park Press. A number of people have published their own ideas about it, including Brumbaugh, without anybody agreeing. A recent publication from Aegean Park Press offers another decryption; I haven't seen that one. If you want *my* guess, it's a hoax made up by Edmund Kelley and an unnamed co-conspirator and sold to Rudolf through the reputation of John Dee (Queen Elizabeth I's astrologer). -- Jim Gillogly {hplabs, ihnp4}!sdcrdcf!randvax!jim jim@rand-unix.arpa I read "Labyrinths of Reason" by William Poundstone recently. I'm posting this to so many newsgroups in part to recommend this book, which, while of a popular nature, gives a good analysis of a wide variety of paradoxes and philosophical quandaries, and is a great read. Anyway, it mentions something called the Voynich manuscript, which is now at Yale University's Beinecke Rare Book and Manuscript Library. It's a real pity that I didn't know about this manuscript and go see it when I was at Yale. The Voynich manuscript is apparently very old. It is a 232-page illuminated manuscript written in a cipher that has never been cracked. (That's what Poundstone says - but see my hypothesis below.) If I may quote Poundstone's charming description, "Its author, subject matter, and meaning are unfathomed mysteries. No one even knows what language the text would be in if you deciphered it. Fanciful picutres of nude women, peculiar inventions, and nonexistent flora and fauna tantalize the would-be decipherer. Color sketches in the exacting style of a medieval herbal depict blossoms and spices that never spring from earth and constellations found in no sky. Plans for weird, otherworldly plumbing show nymphets frolicking in sitz baths connected with elbow-macaroni pipes. The manuscript has the eerie quality of a perfectly sensible book from an alternate universe." There is a picture of one page in Poundstone's book. It's written in a flowing script using "approximately 21 curlicued symbols," some of which are close to the Roman alphabet, but others of which supposedly resemble Cyrillic, Glagolitic, and Ethiopian. There is one tiny note in Middle High German, not necessarily by the original author, talking about the Herbal of Matthiolaus. Some astrology charts in the manuscript have the months labeled in Spanish. "What appears to be a cipher table on the first page has long faded into illegibility," and on the other hand, some scholars have guessed that a barely legible inscription on the *last* page is a key! It is said to have "languished for a long time at the Jesuit College of Mondragone in Frascati, Italy. Then in 1912 it was purchased by Wilfred M. Voynich, a Polish-born scientist and bibliophile... Voynich was the son-in-law of George Boole, the logician..." A letter written in 1666 claims that Holy Roman Emperor Rudolf II of Bohemia (1552-1612) bought the manuscript for 600 gold ducats. He may have bought it from Dr. John Dee, the famous astrologer. Rudolf thought the manuscript was written by Roger Bacon! [Wouldn't it more likely have been written by Dee, out to make a fast ducat?] "Many of the most talented military code breakers of this century have tried to decipher it as a show of prowess. Herbert Yardley, the American code expert who solved the German cipher in WW1 and who cracked a Japanese diplomatic cipher without knowing the Japanese language, failed with the Voynich manuscript. So did John Manly, who unscrambled the Waberski cipher, and William Friedman, who defeated the Japanese "purple code" of the 1940's. Computers have been drafted into the effort in recent years, to no avail." Poundstone goes on to describe a kook, Newbold, who was apparently driven batty in his attempt to crack the manuscript. He then mentions that one Leo Levitov also claimed in 1987 to crack the cipher, saying that it was the text of a 12th-century cult of Isis worshipers, and that it describes a method of euthanasia by opening a vein in a warm bathtub, among other morbid matters. According to Levitov's translation the text begins: "ones treat the dying each the man lying deathly ill the one person who aches Isis each that dies treats the person" Poundstone rejects this translation. According to Poundstone, a William Bennett (see below) has analysed the text with a computer and finds that its entropy is less than any known European language, and closer to those of Polynesian languages. My wild hypothesis, on the basis solely of the evidence above, is this. Perhaps the text was meant to be RANDOM. Of course humans are lousy at generating random sequences. So I'm wondering how attempted random sequences (written in a weird alphabet) would compare statistically with the Voynich manuscript. Anyway, the only source Poundstone seems to cite, other than the manuscript itself, is Leo Levitov's "Solution of the Voynich Manuscript, A Liturgical Manual for the Endura Rite of the Cathari Heresy, the Cult of Isis," Laguna Hills, Calif., Aegean Park Press, 1987, and William Ralph Bennett Jr.'s "Scientific and Engineering Problem-Solving with the Computer," Englewood Cliffs, New Jersey, Prentice-Hall 1976. I will check the Bennett book; the other sounds hard to get ahold of! I would LOVE any further information about this bizarre puzzle. If anyone knows Bennett and can get samples of the Voynich manuscript in electronic form, I would LOVE to get my hands on it. Also, I would appreciate any information on: Voynich The Jesuit College of Mondragone Rudolf II The letter by Rudolf II (where is it? what does it say?) The attempts of Yardley, Friedman and Manly The Herbal of Matthiolaus and, just for the heck of it, the "Waberski cipher" and the "purple code"! This whole business sounds like a quagmire into which angels would fear to tread, but a fool like me finds it fascinating. -- sender's name lost (!?) To counter a few hypotheses that were suggested here: The Voynich Manuscript is certainly not strictly a polyalphabetic cipher like Vigenere or Beaufort or (the one usually called) Porta, because of the frequent repetitions of "words" at intervals that couldn't be multiples of any key length. I suppose one could imagine that it's an interrupted key Vig or something, but common elements appearing at places other than the beginnings of words would seem to rule that out. The I.C. is too high for a digraphic system like (an anachronistic) Playfair in any European language. One of the most interesting Voynich discoveries was made by Prescott Currier, who discovered that the two different "hands" (visually distinct handwriting) used different "dialects": that is, the frequencies for pages written in one hand are different from those written in the other. I confirmed this observation by running some correlation coefficients on the digraph matrices for the two kinds of pages. W. F. Friedman ("The Man Who Broke Purple") thought the Voynich was written in some artificial language. If it's not a hoax, I don't see any evidence to suggest he's wrong. My personal theory (yeah, I've offered too many of those lately) is that it was constructed by Edward Kelley, John Dee's scryer, with somebody else's help (to explain the second handwriting) -- perhaps Dee himself, although he's always struck me as a credulous dupe of Kelley rather than a co-conspirator (cf the Angelic language stuff). The best source I know for the Voynich is Mary D'Imperio's monograph "The Voynich Manuscript: An Elegant Enigma", which is available from Aegean Park Press. -- Jim Gillogly jim@rand.org Here's an update on the Voynich manuscript. This will concentrate on sources for information on the Voynich; later I will write a survey of what I have found out so far. I begin with some references to the case, kindly sent to me by Karl Kluge (the first three) and Micheal Roe <M.Roe@cs.ucl.ac.uk> (the rest). TITLE Thirty-five manuscripts : including the St. Blasien psalter, the Llangattock hours, the Gotha missal, the Roger Bacon (Voynich) cipher ms. Catalogue ; 100 35 manuscripts. CITATION New York, N.Y. : H.P. Kraus, [1962] 86 p., lxvii p. of plates, [1] leaf of plates : ill. (some col.), facsims. ; 36 cm. NOTES "30 years, 1932-1962" ([28] p.) in pocket. Includes indexes. SUBJECT Manuscripts Catalogs. Illumination of books and manuscripts Catalogs. AUTHOR Brumbaugh, Robert Sherrick, 1918- TITLE The most mysterious manuscript : the Voynich "Roger Bacon" cipher manuscript / edited by Robert S. Brumbaugh. CITATION Carbondale : Southern Illinois University Press, c1978. xii, 175 p. : ill. ; 22 cm. SUBJECT Bacon, Roger, 1214?-1294. Ciphers. AUTHOR D'Imperio, M. E. TITLE The Voynich manuscript : an elegant enigma / M. E. D'Imperio. CITATION Fort George E. Mead, Md. : National Security Agency/Central Security Service, 1978. ix, 140 p. : ill. ; 27 cm. NOTES Includes index. Bibliography: p. 124-131. SUBJECT Voynich manuscript. [NOTE: see alternate publisher below!] @book{Bennett76, author = "Bennett, William Ralph", title = "Scientific and Engineering Problem Solving with the Computer", address = "Englewood Cliffs, NJ", publisher = "Prentice-Hall", year = 1976} @book{dImperio78, author = "D'Imperio, M E", title = "The Voynich manuscript: An Elegant Enigma", publisher= "Aegean Park Press", year = 1978} @article{Friedman62, author = "Friedman, Elizebeth Smith", title = "``The Most Mysterious Manuscript'' Still Mysterious", booktitle = "Washington Post", month = "August 5", notes = "Section E", pages = "1,5", year = 1962} @book{Kahn67, author = "Kahn, David", title = "The Codebreakers", publisher = "Macmillan", year = "1967"} @article{Manly31, author = "Manly, John Matthews", title = "Roger Bacon and the Voynich MS", boooktitle = "Speculum VI", pages = "345--91", year = 1931} @article{ONeill44, author = "O'Neill, Hugh", title = "Botanical Remarks on the Voynich MS", journal = "Speculum XIX", pages = "p.126", year = 1944} @book{Poundstone88, author = "Poundstone, W.", title = "Labyrinths of Reason", publisher = "Doubleday", address = "New York", month = "November", year = 1988} @article{Zimanski70, author = "Zimanski, C.", title = "William Friedman and the Voynich Manuscript", journal = "Philological Quarterly", year = "1970"} @article{Guy91b, author = "Guy, J. B. M.", title = "Statistical Properties of Two Folios of the Voynich Manuscript", journal = "Cryptologia", volume = "XV", number = "4", pages = "pp. 207--218", month = "July", year = 1991} @article{Guy91a, author = "Guy, J. B. M.", title = "Letter to the Editor Re Voynich Manuscript", journal = "Cryptologia", volume = "XV", number = "3", pages = "pp. 161--166", year = 1991} This is by no means a complete list. It doesn't include Newbold's (largely discredited) work, nor work by Feely and Stong. In addition, there is the proposed decryption by Leo Levitov (also largely discredited): "Solution of the Voynich Manuscript: A Liturgical Manual for the Endura Rite of the Cathari Heresy, the Cult of Isis_, available from Aegean Park Press, P. O. Box 2837, Laguna Hills CA 92654-0837." According to Earl Boebert, this book is reviewed in Cryptologia XII, 1 (January 1988). I should add that Brumbaugh's book above gives a third, also largely discredited, decryption of the Voynich. According to smb@att.ulysses.com, Aegean Park Press does mail-order business and can be reached at the above address or at 714-586-8811 (an answering machine). Micheal Roe has explained how one get microfilms of the whole manuscript: "The Beinecke Rare Book Library, Yale University sells a microfilm of the manuscript. Their catalog number for the original is MS 408, ``The Voynich `Roger Bacon' Cipher MS''. You should write to them. The British Library [sic - should be Museum] has a photocopy of the MS donated to them by John Manly circa 1931. They apparently lost it until 12 March 1947, when it was entered in the catalogue (without cross-references under Voynich, Manly, Roger Bacon or any other useful keywords...) It appears as ``MS Facs 461: Positive rotographs of a Cipher MS (folios 1-56) acquired in 1912 by Wilfred M. Voynich in Southern Europe.' Correspondance between Newbold, Manly and various British Museum experts appears under ``MS Facs 439: Leaves of the Voynich MS, alleged to be in Roger Bacon's cypher, with correspondence and other pertinent material'' See John Manly's 1931 article in Speculum and Newbold's book for what the correspondance was about! There are also a number of press cuttings. Both of these in are in the manuscript collection, for which special permission is needed in addition to a normal British Library reader's pass." Also, Jim Gillogly has been extremely kind in making available part of the manuscript that was transcribed and keyed in by Mary D'Imperio (see above), using Prescott Currier's notation. It appears to consist of 166 of the total 232 pages. I hope to do some statistical studies on this, and I encourage others to do the same and let me know what they find! As Jim notes, the file is pub/jim/voynich.tar.Z and is available by anonymous ftp at rand.org. I've had a little trouble with this file at page 165, where I read "1650voynich 664" etc., with page 166 missing. If anyone else notes this let Jim or I know. Jim says he has confirmed by correlations between digraph matrices the discovery by Prescott Crurrier that the manuscript is written in two visibly distinct hands. These are marked "A" and "B" in the file voynich.tar.Z. Because of the possibility that the Voynich is nonsense, it would be interesting to compare the Voynich to the Codex Seraphinianus, which Kevin McCarty kindly reminded me of. He writes: "This is very odd. I know nothing of the Voynich manuscript, but I know of something which sounds very much like it and was created by an Italian artist, who it now seems was probably influenced by this work. It a book titled "Codex Seraphinianus", written in a very strange script. The title page contains only the book's title and the publisher's name: Abbeville Press, New York. The only clues in English (in *any* recognizable language) are some blurbs on the dust jacket that identify it as a modern work of art, and the copyright notice, in fine print, which reads "Library of Congress Cataloging in Publication Data Serafini, Luigi. Codex Seraphinianus. 1. Imaginary Languages. 2. Imaginary societies. 3. Encyclopedias and Dictionaries-- Miscellanea. I. Title. PN6381.S4 1983 818'.5407 83.-7076 ISBN 0-89659-428-9 First American Edition, 1983. Copyright (c) 1981 by Franco Maria Ricci. All rights reserved by Abbeville Press. No part of this book may be reproduced... without permission in writing from the publisher. Inquiries should be addressed to Abbeville Press, Inc., 505 Park Avenue, New York 10022. Printed and bound in Italy." The book is remarkable and bizarre. It *looks* like an encyclopedia for an imaginary world. Page after page of beautiful pictures of imaginary flora and fauna, with annotations and captions in a completely strange script. Machines, architecture, umm, 'situations', arcane diagrams, implements, an archeologist pointing at a Rosetta stone (with phony hieroglyphics), an article on penmanship (with unorthodox pens), and much more, finally ending with a brief index. The script in this work looks vaguely similar to the Voynich orthography shown in Poundstone's book (I just compared them); the alphabets look quite similar, but the Codex script is more cursive and less bookish than Voynich. It runs to about 200 pages, and probably ought to provide someone two things: - a possible explanation of what the Voynich manuscript is (a highly imaginative work of art) - a textual work which looks like it was inspired by it and might provide an interesting comparison for statistical study." I suppose it would be too much to hope that someone has already transcribed parts of the Codex, but nonetheless, if anyone has any in electronic form, I would love to have a copy for comparative statistics. Jacques Guy kindly summarized his analysis (in Cryptologia, see above) of the Voynich as follows: "I transcribed the two folios in Bennett's book and submitted them to letter-frequency counts, distinguishing word-initial, word-medial, word-final, isolated, line-initial, and line-final positions. I also submitted that transcription to Sukhotin's algorithm which, given a text written in an alphabetical system, identifies which symbols are vowels and which are consonants. The letter transcribed CT in Bennett's system came out as a consonant, the one transcribed CC as vowel. Now it so happens that CT is exactly the shape of the letter "t" in the Beneventan script (used in medieval Spain and Northern Italy), and CC is exactly the shape of "a" in that same script. I concluded that the author had a knowledge of that script, and that the values of CT and CC probably were "t" and "a". There's a lot more, but more shaky." By popular demand I've put a machine-readable copy of the Voynich Manuscript up for anonymous ftp: Host: rand.org File: pub/jim/voynich.tar.Z It uses Prescott Currier's notation, and was transcribed by Mary D'Imperio. If you use it in any analysis, be sure to give credit to D'Imperio, who put in a lot of effort to get it right. -- Jim Gillogly jim@rand.org This post is essentially a summary of the fruit of a short research quest at the local library. Brief description of the Voynich manuscript: The Voynich manuscript was bought (in about 1586) by the Holy Roman Emperor Rudolf II. He believed it to be the work of Roger Bacon an english 13th century philosopher. The manuscript consisted of about 200 pages with many illustrations. It is believed that the manuscript contains some secret scientific or magical knowledge since it is entirely written in secret writing (presumably in cipher). The Voynich Manuscript is often abbreviated "Voynich MS" in all of the books I have read on Voynich. This is done without explanation. I suppose it is just a convention started by the founding analysts of the manuscript to call it that. William R. Newbold, one of the original analysts of the Voynich MS after Voynich, claims to have arrived at a partial decipherment of the entire manuscript. His book The Cipher of Roger Bacon [2] contains a history of the unravelment of the cipher *and* keys to the cipher itself. As well as translations of several pages of the manuscript. Newbold derives his decipherment rules through a study of the medeival mind (which he is a leading scholar in) as well as the other writings of Roger Bacon. Says Newbold, ciphers in Roger Bacon's writings are not new, as Bacon discusses in other works the need for monks to use encipherment to protect their knowlege. Newbold includes many partial decipherments from the Voynich MS but most of them are presented in Latin only. Newbolds deciphering rules (from The Cipher of Roger Bacon [1]) --------------------------------------------------------------- 1. Syllabification: [double all but the first and last letters of each word, and divide the product into biliteral groups or symbols.] 2. Translation: [translate these symbols into the alphabetic values] 3. Reversion: [change the alphabetic values to the phonetic values, by use of the reversion alphabet] 4. Recomposition: [ rearrange the letters in order, and thus recompose the true text]. The text I copied this from failed to note step 0 which was: 0. Ignore. [ignore the actual shape of every symbol and analyze only the (random?) properties of the direction of swirl and crosshatch patterns of the characters when viewed under a microscope. 14 distinct contruction patterns can be identified among the (much larger) set of symbols] John M. Manly in The Most Mysterious Manuscript [3], suggests that Newbold's method of decipherment is totally invalid. Manly goes on to show that it is not difficult to obtain *ANY DESIRABLE* message from the Voynich MS using Newbold's rules. He shows that after fifteen minutes deciphering a short sequence of letters he arrives at the plaintext message "Paris is lured into loving vestals..." and quips that he will furnish a continuation of the translation upon request! The reason I have spent so much time explaining Newbold's method is that Newbold presents the most convincing argument for how he arrived at his conclusions. Notwithstanding the fact that he invented the oija board of deciphering systems. Joseph Martin Feely, in his book on the Voynich MS [2] , claims to have found the key to deciphering at least one page of the Voynich MS. His entire book on the topic of the Voynich manuscript is devoted to the deciphering of the single page 78. Feely presents full tables of translation of the page 78 from its written form into latin (and english). It seems that Feely was using the exhaustive analysis method to determine the key. Feely suggests the following translation of (the first fiew lines of) page 78 of the Voynich MS: "the combined stream when well humidified, ramifies; afterward it is broken down smaller; afterward, at a distance, into the fore-bladder it comes [1]. Then vesselled, it is after-a-while ruminated: well humidified it is clothed with veinlets [2]. Thence after-a-bit they move down; tiny teats they provide (or live upon) in the outpimpling of the veinlets. They are impermiated; are thrown down below; they are ruminated; they are feminized with the tiny teats. .... " ... and so on for three more pages of "english plaintext". The descriptions by Feely say that this text is accompanied in the Voynich MS by an illustration that (he says) is unmistakably the internal female reproductive organs (I saw the plate myself and they DO look like fallopian tubes *AFTER* I read the explanation). The most informative work that I found (I feel) was "The Most Mysterious Manuscript". Of the five books on Voynich that I found, this was the only one that didn't claim to have found the key but was, rather, a collection of essays on the history of the Voynich MS and criticisms of various attempts by earlier scientists. It was also the *latest* book that I was able to consult, being published in 1978. My impression from the black and white plates of the Voynich MS I've seen, are that the illustrations are very weird when compared to other 'illuminated' manuscripts of this time. Particularly I would say that there is emphasis on the female nude that is unusual for the art of this period. I can't say that I myself believe the images to have ANYTHING to do with the text. My own conjecture is that the manuscript is a one-way encipherment. A cipher so clever that the inventor didn't even think of how it could be deciphered. Sorta like an /etc/passwd file. Bibliography ------------ 1. William R. Newbold. _The Cipher of Roger Bacon_Roland G Kent, ed. University of Pennsylvania Press, 1928. 2. Joseph Martin Feely. _Roger Bacon's Cipher: The Right Key Found_ Rochester N.Y.:Joseph Martin Feely, pub., 1943. 3. _The Most Mysterious Manuscript_ Robert S. Brumbaugh, ed. Southern Illinois Press, 1978 Unix filters are so wonderful. Massaging the machine readable file, we find: 4182 "words", of which 1284 are used more than once, 308 used 8+ times, 184 used 15+ times, 23 used 100+ times. Does this tell us anything about the language (if any) the text is written in? For those who may be interested, here are the 23 words used 100+ times: 121 2 115 4OFAE 114 4OFAM 155 4OFAN 195 4OFC89 162 4OFCC89 101 4OFCC9 189 89 111 8AE 492 8AM 134 8AN 156 8AR 248 OE 148 OR 111 S9 251 SC89 142 SC9 238 SOE 150 SOR 244 ZC89 116 ZC9 116 ZOE Could someone email the Voynich Ms. ref list that appeared here not very long ago? Thanks in advance... Also... I came across the following ref that is fun(?): The Voynich manuscript: an elegant enigma / M. E. D'Imperio Fort George E. Mead, Md. : National Security Agency(!) Central Security Service(?), 1978. ix, 140 p. : ill. ; 27 cm. The (?!) are mine... Sorry if this was already on the list, but the mention of the NSA (and what's the CSS?) made it jump out at me... -- Ron Carter | rcarter@nyx.cs.du.edu rcarter GEnie 70707.3047 CIS Director | Center for the Study of Creative Intelligence Denver, CO | Knowledge is power. Knowledge to the people. Just say know. Distribution: na Organization: Wetware Diversions, San Francisco Keywords: From sci.archaeology: >From: jamie@cs.sfu.ca (Jamie Andrews) >Date: 16 Nov 91 00:49:08 GMT > > It seems like the person who would be most likely to solve >this Voynich manuscript cipher would have >(a) knowledge of the modern techniques for solving more complex > ciphers such as Playfairs and Vigineres; and >(b) knowledge of the possible contemporary and archaic languages > in which the plaintext could have been written. An extended discussion of the Voynich Manuscript may be found in the tape of the same name by Terence McKenna. I'm not sure who is currently publishing this particular McKenna tape but probably one of: Dolphin Tapes, POB 71, Big Sur, CA 93920 Sounds True, 1825 Pearl St., Boulder, CO 80302 Sound Photosynthesis, POB 2111, Mill Valley, CA 94942 The Spring 1988 issue of Gnosis magazine contained an article by McKenna giving some background of the Voynich Manuscipt and attempts to decipher it, and reviewing Leo Levitov's "Solution of the Voynich Manuscript" (published in 1987 by Aegean Park Press, POB 2837 Laguna Hills, CA 92654). Levitov's thesis is that the manuscript is the only surviving primary document of the Cathar faith (exterminated on the orders of the Pope in the Albigensian Crusade in the 1230s) and that it is in fact not encrypted material but rather is a highly polyglot form of Medieval Flemish with a large number of Old French and Old High German loan words, written in a special script. As far as I know Levitov's there has been no challenge to Levitov's claims so far. Michael Barlow, who had reviewed Levitov's book in Cryptologia, had sent me photocopies of the pages where much of the language was described (pp.21-31). I have just found them, and am looking at them now as I am typing this. Incidentally, I do not believe this has anything to do with cryptology proper, but the decipherment of texts in unknown languages. So if you are into cryptography proper, skip this. Looking at the "Voynich alphabet" pp.25-27, I made a list of the letters of the Voynich language as Levitov interprets them, and I added phonetic descriptions of the sounds I *think* Levitov meant to describe. Here it is: Letter# Phonetic Phonetic descriptions (IPA) in linguists' jargon: in plain English: 1 a low open, central unrounded a as in father e mid close, front, unrounded ay as in May O mid open, back, rounded aw as in law or o as in got (British pronunciation) 2 s unvoiced dental fricative s as in so 3 d voiced dental stop d 4 E mid, front, unrounded e as in wet 5 f unvoiced labiodental fricative f 6 i short, high open, front, i as in dim unrounded 7 i: long, high, front, unrounded ea as in weak 8 i:E (?) I can't make head nor tail of Levitov's explanations. Probably like "ei" in "weird" dragging along the "e": "weeeird"! (British pronunciation, with a silent "r") 9 C unvoiced palatal fricative ch in German ich 10 k unvoived velar stop k 11 l lateral, can't be more precise from description, probably like l in "loony" 12 m voiced bilabial nasal m 13 n voiced dental nasal n 14 r (?) cannot tell precisely from Scottish r? description Dutch r? 15 t no description; dental stop? t 16 t another form for #15 t 17 T (?) no description th as in this? th as in thick? 18 TE (?) again, no description or ET (?) 19 v voiced labiodental fricative v as in rave 20 v ditto, same as #19 ditto (By now, you will have guessed what my conclusion about Levitov's decipherment was) In the column headed "Phonetic (IPA)" I have used capital letters for lack of the special international phonetic symbols: E for the Greek letter "epsilon" O for the letter that looks like a mirror-image of "c" C for c-cedilla T for the Greek letter "theta" The colon (:) means that the sound represented by the preceding letter is long, e.g. "i:" is a long "i". The rest, #21 to 25, are not "letters" proper, but represent groups of two or more letters, just like #18 does. They are: 21 av 22a Ev 22b vE 23 CET 24 kET 25 sET That gives us a language with 6 vowels: a (#1), e (#1 again), O (#1 again), E (#4), i (#6), and i: (#7). Letter #8 is not a vowel, but a combination of two vowels: i: (#7) and probably E (#4). Levitov writes that the language is derived from Dutch. If so, it has lost the "oo" sound (English spelling; "oe" in Dutch spelling), and the three front rounded vowels of Dutch: u as in U ("you", polite), eu as in deur ("door"), u as in vlug ("quick"). Note that out of six vowels, three are confused under the same letter (#1), even though they sound very different from one another: a, e, O. Just imagine that you had no way of distinguishing between "last", "lest" and "lost" when writing in English, and you'll have a fair idea of the consequences. Let us look at the consonants now. I will put them in a matrix, with the points of articulation in one dimension, and the manner of articulation in the other (it's all standard procedure when analyzing a language). Brackets around a letter will mean that I could not tell where to place it exactly, and just took a guess. labial dental palatal velar nasal m n voiced stop d unvoiced stop t k voiced fricative v (T) unvoiced fricative f s C lateral l trill (?) (r) Note that there are only twelve consonant sounds. That is unheard of for a European language. No European language has so few consonant sounds. Spanish, which has very few sounds (only five vowels), has seventeen distinct consonants sounds, plus two semi-consonants. Dutch has from 18 to 20 consonants (depending on speakers, and how you analyze the sounds. Warning: I just counted them on the back of an envelope; I might have missed one or two). What is also extraordinary in Levitov's language is that it lacks a "g", and *BOTH* "b" and "p". I cannot think of one single language in the world that lacks both "b" and "p". Levitov also says that "m" occurs only word-finally, never at the beginning, nor in the middle of a word. That's true: the letter he says is an "m" is always word-final in the reproductions I have seen of the Voynich MS. But no language I know of behaves like that. All have an "m" (except one American Indian language, which is very famous for that, and the name of which escapes me right now), but, if there is a position where "m" never appears in some languages, that position is word-finally. Exactly the reverse of Levitov's language. What does Levitov say about the origin of the language? "The language was very much standardized. It was an application of a polyglot oral tongue into a literary language which would be understandable to people who did not understand Latin and to whom this language could be read." At first reading, I would dismiss it all as nonsense: "polyglot oral tongue" means nothing in linguistics terms. But Levitov is a medical doctor, so allowances must be made. The best meaning I can read into "polyglot oral tongue" is "a language that had never been written before and which had taken words from many different languages". That is perfectly reasonable: English for one, has done that. Half its vocabulary is Norman French, and some of the commonest words have non-Anglo-Saxon origins. "Sky", for instance, is a Danish word. So far, so good. Levitov continues: "The Voynich is actually a simple language because it follows set rules and has a very limited vocabulary.... There is a deliberate duality and plurality of words in the Voynich and much use of apostrophism". By "duality and plurality of words" Levitov means that the words are highly ambiguous, most words having two or more different meanings. I can only guess at what he means by apostrophism: running words together, leaving bits out, as we do in English: can not --> cannot --> can't, is not --> ain't. Time for a tutorial in the Voynich language as I could piece it together from Levitov's description. Because, according to Levitov, letter #1 represent 3 vowels sounds, I will represent it by just "a", but remember: it can be pronounced a, e, or o. But I will distinguish, as does Levitov, between the two letters which he says were both pronounced "v", using "v" for letter #20 and "w" for letter #21. Some vocabulary now. Some verbs first, which Levitov gives in the infinitive. In the Voynich language the infinitive of verbs ends in -en, just like in Dutch and in German. I have removed that grammatical ending in the list which follows, and given probable etymologies in parentheses (Levitov gives doesn't give any): ad = to aid, help ("aid") ak = to ache, pain ("ache") al = to ail ("ail") and = to undergo the "Endura" rite ("End[ura]", probably) d = to die ("d[ie]") fad = to be for help (from f= for and ad=aid) fal = to fail ("fail") fil = to be for illness (from: f=for and il=ill) il = to be ill ("ill") k = to understand ("ken", Dutch and German "kennen" meaning "to know") l = to lie deathly ill, in extremis ("lie", "lay") s = to see ("see", Dutch "zien") t = to do, treat (German "tun" = to do) v = to will ("will" or Latin "volo" perhaps) vid = to be with death (from vi=with and d=die) vil = to want, wish, desire (German "willen") vis = to know ("wit", German "wissen", Dutch "weten") vit = to know (ditto) viT = to use (no idea, Latin "uti" perhaps?) vi = to be the way (Latin "via") eC = to be each ("each") ai:a = to eye, look at ("eye", "oog" in Dutch) en = to do (no idea) Example given by Levitov: enden "to do to death" made up of "en" (to do), "d" (to die) and "en" (infinitive ending). Well, to me, that's doing it the hard way. What's wrong with just "enden" = to end (German "enden", too!) More vocabulary: em = he or they (masculine) ("him") er = her or they (feminine) ("her") eT = it or they ("it" or perhaps "they" or Dutch "het") an = one ("one", Dutch "een") "There are no declensions of nouns or conjugation of verbs. Only the present tense is used" says Levitov. Examples: den = to die (infinitive) (d = die, -en = infinitive) deT = it/they die (d = die, eT = it/they) diteT = it does die (d = die, t = do, eT = it/they, with an "i" added to make it easier to pronounce, which is quite common and natural in languages) But Levitov contradicts himself immediately, giving another tense (known as present progressive in English grammar): dieT = it is dying But I may be unfair there, perhaps it is a compound: d = die, i = is ...-ing, eT = it/they. Plurals are formed by suffixing "s" in one part of the MS, "eT" in another: "ans" or "aneT" = ones. More: wians = we ones (wi = we, wie in Dutch, an = one, s = plural) vian = one way (vi = way, an = one) wia = one who (wi = who, a = one) va = one will (v = will, a = one) wa = who wi = who wieT = who, it (wi = who, eT = it) witeT = who does it (wi = who, t = do, eT = it/they) weT = who it is (wi = who, eT = it, then loss of "i", giving "weT") ker = she understands (k = understand, er =she) At this stage I would like to comment that we are here in the presence of a Germanic language which behaves very, very strangely in the way of the meanings of its compound words. For instance, "viden" (to be with death) is made up of the words for "with", "die" and the infinitive suffix. I am sure that Levitov here was thinking of a construction like German "mitkommen" which means "to come along" (to "withcome"). I suppose I could say "Bitte, sterben Sie mit" on the same model as "Bitte, kommen Sie mit" ("Come with me/us, please), thereby making up a verb "mitsterben", but that would mean "to die together with someone else", not "to be with death". Let us see how Levitov translates a whole sentence. Since he does not explain how he breaks up those compound words I have tried to do it using the vocabulary and grammar he provides in those pages. My tentative explanations are in parenthesis. TanvieT faditeT wan aTviteT anTviteT atwiteT aneT TanvieT = the one way (T = the (?), an = one, vi =way, eT = it) faditeT = doing for help (f = for, ad = aid, i = -ing, t = do, eT = it) wan = person (wi/wa = who, an = one) aTviteT = one that one knows (a = one, T = that, vit = know, eT = it. Here, Levitov adds one extra letter which is not in the text, getting "aTaviteT", which provide the second "one" of his translation) anTviteT = one that knows (an =one, T = that, vit = know, eT = it) atwiteT = one treats one who does it (a = one, t = do, wi = who, t = do, eT = it. Literally: "one does [one] who does it". The first "do" is translated as "treat", the second "one" is added in by Levitov: he added one letter, which gives him "atawiteT") aneT = ones (an = one, -eT = the plural ending) Levitov's translation of the above in better English: "the one way for helping a person who needs it, is to know one of the ones who do treat one". Need I say more? Does anyone still believe that Levitov's translations are worth anything? As an exercise, here is the last sentence on p.31, with its word-for-word translation by Levitov. I leave you to work it out, and to figure out what it might possibly mean. Good luck! tvieT nwn anvit fadan van aleC tvieT = do the ways nwn = not who does (but Levitov adds a letter to make it "nwen") anvit = one knows fadan = one for help van = one will aleC = each ail ==> cryptology/swiss.colony.p <== What are the 1987 Swiss Colony ciphers? ==> cryptology/swiss.colony.s <== Did anyone solve the 1987 'Crypto-gift' contest that was run by Swiss Colony? My friend and I worked on it for 4 months, but didn't get anywhere. My friend solved the 1986 puzzle in about a week and won $1000. I fear that we missed some clue that makes it incredibly easy to solve. I'm including the code, clues and a few notes for those of you so inclined to give it a shot. 197,333,318,511,824, 864,864,457,197,333, 824,769,372,769,864, 865,457,153,824,511,223,845,318, 489,953,234,769,703,489,845,703, 372,216,457,509,333,153,845,333, 511,864,621,611,769,707,153,333, 703,197,845,769,372,621,223,333, 197,845,489,953,223,769,216,223, 769,769,457,153,824,511,372,223, 769,824,824,216,865,845,153,769, 333,704,511,457,153,333,824,333, 953,372,621,234,953,234,865,703, 318,223,333,489,944,153,824,769, 318,457,234,845,318,223,372,769, 216,894,153,333,511,611, 769,704,511,153,372,621, 197,894,894,153,333,953, 234,845,318,223 CHRIS IS BACK WITH GOLD FOR YOU HIS RHYMES CONTAIN THE SECRET. YOU SCOUTS WHO'VE EARNED YOUR MERIT BADGE WILL QUICKLY LEARN TO READ IT. SO WHEN YOUR CHRISTMAS HAM'S ALL GONE AND YOU'RE READY FOR THE TUSSLE, BALL UP YOUR HAND INTO A FIST AND SHOW OUR MOUSE YOUR MUSCLE. PLEASE READ THESE CLUES WE LEAVE TO YOU BOTH FINE ONES AND THE COARSE; IF CARE IS USED TO HEED THEM ALL YOU'LL SUFFER NO REMORSE. Notes: The puzzle comes as a jigsaw that when assembled has the list of numbers. They are arranged as indicated on the puzzle, with commas. The lower right corner has a drawing of 'Secret Agent Chris Mouse'. He holds a box under his arm which looks like the box the puzzle comes in. The upper left corner has the words 'NEW 1987 $50,000 Puzzle'. The lower left corner is empty. The clues are printed on the entry form in upper case, with the punctuation as shown. Ed Rupp ...!ut-sally!oakhill!ed Motorola, Inc., Austin Tx. ==> decision/allais.p <== The Allais Paradox involves the choice between two alternatives: A. 89% chance of an unknown amount 10% chance of $1 million 1% chance of $1 million B. 89% chance of an unknown amount (the same amount as in A) 10% chance of $2.5 million 1% chance of nothing What is the rational choice? Does this choice remain the same if the unknown amount is $1 million? If it is nothing? ==> decision/allais.s <== This is "Allais' Paradox". Which choice is rational depends upon the subjective value of money. Many people are risk averse, and prefer the better chance of $1 million of option A. This choice is firm when the unknown amount is $1 million, but seems to waver as the amount falls to nothing. In the latter case, the risk averse person favors B because there is not much difference between 10% and 11%, but there is a big difference between $1 million and $2.5 million. Thus the choice between A and B depends upon the unknown amount, even though it is the same unknown amount independent of the choice. This violates the "independence axiom" that rational choice between two alternatives should depend only upon how those two alternatives differ. However, if the amounts involved in the problem are reduced to tens of dollars instead of millions of dollars, people's behavior tends to fall back in line with the axioms of rational choice. People tend to choose option B regardless of the unknown amount. Perhaps when presented with such huge numbers, people begin to calculate qualitatively. For example, if the unknown amount is $1 million the options are: A. a fortune, guaranteed B. a fortune, almost guaranteed a tiny chance of nothing Then the choice of A is rational. However, if the unknown amount is nothing, the options are: A. small chance of a fortune ($1 million) large chance of nothing B. small chance of a larger fortune ($2.5 million) large chance of nothing In this case, the choice of B is rational. The Allais Paradox then results from the limited ability to rationally calculate with such unusual quantities. The brain is not a calculator and rational calculations may rely on things like training, experience, and analogy, none of which would be help in this case. This hypothesis could be tested by studying the correlation between paradoxical behavior and "unusualness" of the amounts involved. If this explanation is correct, then the Paradox amounts to little more than the observation that the brain is an imperfect rational engine. ==> decision/division.p <== N-Person Fair Division If two people want to divide a pie but do not trust each other, they can still ensure that each gets a fair share by using the technique that one person cuts and the other person chooses. Generalize this technique to more than two people. Take care to ensure that no one can be cheated by a coalition of the others. ==> decision/division.s <== N-Person Fair Division Number the people from 1 to N. Person 1 cuts off a piece of the pie. Person 2 can either diminish the size of the cut off piece or pass. The same for persons 3 through N. The last person to touch the piece must take it and is removed from the process. Repeat this procedure with the remaining N - 1 people, until everyone has a piece. (cf. Luce and Raiffa, "Games and Decisions", Wiley, 1957, p. 366) There is a cute result in combinatorics called the Marriage Theorem. A village has n men and n women, such that for all 0 < k <= n and for any set of k men there are at least k women, each of whom is in love with at least one of the k men. All of the men are in love with all of the women :-}. The theorem asserts that there is a way to arrange the village into n monogamous couplings. The Marriage Theorem can be applied to the Fair Pie-Cutting Problem. One player cuts the pie into n pieces. Each of the players labels some non-null subset of the pieces as acceptable to him. For reasons given below he should "accept" each piece of size > 1/n, not just the best piece(s). The pie-cutter is required to "accept" all of the pieces. Given a set S of players let S' denote the set of pie-pieces acceptable to at least one player in S. Let t be the size of the largest set (T) of players satisfying |T| > |T'|. If there is no such set, the Marriage Theorem can be applied directly. Since the pie-cutter accepts every piece we know that t < n. Choose |T| - |T'| pieces at random from outside T', glue them together with the pieces in T' and let the players in T repeat the game with this smaller (t/n)-size pie. This is fair since they all rejected the other n-t pieces, so they believe this pie is larger than t/n. The remaining n-t players can each be assigned one of the remaining n-t pie-pieces without further ado due to the Marriage Theorem. (Otherwise the set T above was not maximal.) ==> decision/dowry.p <== Sultan's Dowry A sultan has granted a commoner a chance to marry one of his hundred daughters. The commoner will be presented the daughters one at a time. When a daughter is presented, the commoner will be told the daughter's dowry. The commoner has only one chance to accept or reject each daughter; he cannot return to a previously rejected daughter. The sultan's catch is that the commoner may only marry the daughter with the highest dowry. What is the commoner's best strategy assuming he knows nothing about the distribution of dowries? ==> decision/dowry.s <== Solution Since the commoner knows nothing about the distribution of the dowries, the best strategy is to wait until a certain number of daughters have been presented then pick the highest dowry thereafter. The exact number to skip is determined by the condition that the odds that the highest dowry has already been seen is just greater than the odds that it remains to be seen AND THAT IF IT IS SEEN IT WILL BE PICKED. This amounts to finding the smallest x such that: x/n > x/n * (1/(x+1) + ... + 1/(n-1)). Working out the math for n=100 and calculating the probability gives: The commoner should wait until he has seen 37 of the daughters, then pick the first daughter with a dowry that is bigger than any preceding dowry. With this strategy, his odds of choosing the daughter with the highest dowry are surprisingly high: about 37%. (cf. F. Mosteller, "Fifty Challenging Problems in Probability with Solutions", Addison-Wesley, 1965, #47; "Mathematical Plums", edited by Ross Honsberger, pp. 104-110) ==> decision/envelope.p <== Someone has prepared two envelopes containing money. One contains twice as much money as the other. You have decided to pick one envelope, but then the following argument occurs to you: Suppose my chosen envelope contains $X, then the other envelope either contains $X/2 or $2X. Both cases are equally likely, so my expectation if I take the other envelope is .5 * $X/2 + .5 * $2X = $1.25X, which is higher than my current $X, so I should change my mind and take the other envelope. But then I can apply the argument all over again. Something is wrong here! Where did I go wrong? In a variant of this problem, you are allowed to peek into the envelope you chose before finally settling on it. Suppose that when you peek you see $100. Should you switch now? ==> decision/envelope.s <== Let's follow the argument carefully, substituting real numbers for variables, to see where we went wrong. In the following, we will assume the envelopes contain $100 and $200. We will consider the two equally likely cases separately, then average the results. First, take the case that X=$100. "I have $100 in my hand. If I exchange I get $200. The value of the exchange is $200. The value from not exchanging is $100. Therefore, I gain $100 by exchanging." Second, take the case that X=$200. "I have $200 in my hand. If I exchange I get $100. The value of the exchange is $100. The value from not exchanging is $200. Therefore, I lose $100 by exchanging." Now, averaging the two cases, I see that the expected gain is zero. So where is the slip up? In one case, switching gets X/2 ($100), in the other case, switching gets 2X ($200), but X is different in the two cases, and I can't simply average the two different X's to get 1.25X. I can average the two numbers ($100 and $200) to get $150, the expected value of switching, which is also the expected value of not switching, but I cannot under any circumstances average X/2 and 2X. This is a classic case of confusing variables with constants. OK, so let's consider the case in which I looked into the envelope and found that it contained $100. This pins down what X is: a constant. Now the argument is that the odds of $50 is .5 and the odds of $200 is .5, so the expected value of switching is $125, so we should switch. However, the only way the odds of $50 could be .5 and the odds of $200 could be .5 is if all integer values are equally likely. But any probability distribution that is finite and equal for all integers would sum to infinity, not one as it must to be a probability distribution. Thus, the assumption of equal likelihood for all integer values is self-contradictory, and leads to the invalid proof that you should always switch. This is reminiscent of the plethora of proofs that 0=1; they always involve some illegitimate assumption, such as the validity of division by zero. Limiting the maximum value in the envelopes removes the self-contradiction and the argument for switching. Let's see how this works. Suppose all amounts up to $1 trillion were equally likely to be found in the first envelope, and all amounts beyond that would never appear. Then for small amounts one should indeed switch, but not for amounts above $500 billion. The strategy of always switching would pay off for most reasonable amounts but would lead to disastrous losses for large amounts, and the two would balance each other out. For those who would prefer to see this worked out in detail: Assume the smaller envelope is uniform on [$0,$M], for some value of $M. What is the expectation value of always switching? A quarter of the time $100 >= $M (i.e. 50% chance $X is in [$M/2,$M] and 50% chance the larger envelope is chosen). In this case the expected switching gain is -$50 (a loss). Thus overall the always switch policy has an expected (relative to $100) gain of (3/4)*$50 + (1/4)*(-$50) = $25. However the expected absolute gain (in terms of M) is: / M | g f(g) dg, [ where f(g) = (1/2)*Uniform[0,M)(g) + /-M (1/2)*Uniform(-M,0](g). ] = 0. QED. OK, so always switching is not the optimal switching strategy. Surely there must be some strategy that takes advantage of the fact that we looked into the envelope and we know something we did not know before we looked. Well, if we know the maximum value $M that can be in the smaller envelope, then the optimal decision criterion is to switch if $100 < $M, otherwise stick. The reason for the stick case is straightforward. The reason for the switch case is due to the pdf of the smaller envelope being twice as high as that of the larger envelope over the range [0,$M). That is, the expected gain in switching is (2/3)*$100 + (1/3)*(-$50) = $50. What if we do not know the maximum value of the pdf? You can exploit the "test value" technique to improve your chances. The trick here is to pick a test value T. If the amount in the envelope is less than the test value, switch; if it is more, do not. This works in that if T happens to be in the range [M,2M] you will make the correct decision. Therefore, assuming the unknown pdf is uniform on [0,M], you are slightly better off with this technique. Of course, the pdf may not even be uniform, so the "test value" technique may not offer much of an advantage. If you are allowed to play the game repeatedly, you can estimate the pdf, but that is another story... ==> decision/exchange.p <== At one time, the Mexican and American dollars were devalued by 10 cents on each side of the border (i.e. a Mexican dollar was 90 cents in the US, and a US dollar was worth 90 cents in Mexico). A man walks into a bar on the American side of the border, orders 10 cents worth of beer, and tenders a Mexican dollar in change. He then walks across the border to Mexico, orders 10 cents worth of beer and tenders a US dollar in change. He continues this throughout the day, and ends up dead drunk with the original dollar in his pocket. Who pays for the drinks? ==> decision/exchange.s <== The man paid for all the drinks. But, you say, he ended up with the same amount of money that he started with! However, as he transported Mexican dollars into Mexico and US dollars into the US, he performed "economic work" by moving the currency to a location where it was in greater demand (and thus valued higher). The earnings from this work were spent on the drinks. Note that he can only continue to do this until the Mexican bar runs out of US dollars, or the US bar runs out of Mexican dollars, i.e., until he runs out of "work" to do. ==> decision/newcomb.p <== Newcomb's Problem A being put one thousand dollars in box A and either zero or one million dollars in box B and presents you with two choices: (1) Open box B only. (2) Open both box A and B. The being put money in box B only if it predicted you will choose option (1). The being put nothing in box B if it predicted you will do anything other than choose option (1) (including choosing option (2), flipping a coin, etc.). Assuming that you have never known the being to be wrong in predicting your actions, which option should you choose to maximize the amount of money you get? ==> decision/newcomb.s <== This is "Newcomb's Paradox". You are presented with two boxes: one certainly contains $1000 and the other might contain $1 million. You can either take one box or both. You cannot change what is in the boxes. Therefore, to maximize your gain you should take both boxes. However, it might be argued that you can change the probability that the $1 million is there. Since there is no way to change whether the million is in the box or not, what does it mean that you can change the probability that the million is in the box? It means that your choice is correlated with the state of the box. Events which proceed from a common cause are correlated. My mental states lead to my choice and, very probably, to the state of the box. Therefore my choice and the state of the box are highly correlated. In this sense, my choice changes the "probability" that the money is in the box. However, since your choice cannot change the state of the box, this correlation is irrelevant. The following argument might be made: your expected gain if you take both boxes is (nearly) $1000, whereas your expected gain if you take one box is (nearly) $1 million, therefore you should take one box. However, this argument is fallacious. In order to compute the expected gain, one would use the formulas: E(take one) = $0 * P(predict take both | take one) + $1,000,000 * P(predict take one | take one) E(take both) = $1,000 * P(predict take both | take both) + $1,001,000 * P(predict take one | take both) While you are given that P(do X | predict X) is high, it is not given that P(predict X | do X) is high. Indeed, specifying that P(predict X | do X) is high would be equivalent to specifying that the being could use magic (or reverse causality) to fill the boxes. Therefore, the expected gain from either action cannot be determined from the information given. ==> decision/prisoners.p <== Three prisoners on death row are told that one of them has been chosen at random for execution the next day, but the other two are to be freed. One privately begs the warden to at least tell him the name of one other prisoner who will be freed. The warden relents: 'Susie will go free.' Horrified, the first prisoner says that because he is now one of only two remaining prisoners at risk, his chances of execution have risen from one-third to one-half! Should the warden have kept his mouth shut? ==> decision/prisoners.s <== Each prisoner had an equal chance of being the one chosen to be executed. So we have three cases: Prisoner executed: A B C Probability of this case: 1/3 1/3 1/3 Now, if A is to be executed, the warden will randomly choose either B or C, and tell A that name. When B or C is the one to be executed, there is only one prisoner other than A who will not be executed, and the warden will always give that name. So now we have: Prisoner executed: A A B C Name given to A: B C C B Probability: 1/6 1/6 1/3 1/3 We can calculate all this without knowing the warden's answer. When he tells us B will not be executed, we eliminate the middle two choices above. Now, among the two remaining cases, C is twice as likely as A to be the one executed. Thus, the probability that A will be executed is still 1/3, and C's chances are 2/3.