Communication with Extrate~Restrial "Intelligence1 by LAMBROS D

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UNCLASSIFIED

Communication _with Extrate~restrial "Intelligence1 BY LAMBROS D. CAI.i:.IMAHOS

. ; U~ified:··· ..... ·-

We are not alone in the universe. A few years ago, this notion - seemed farfetched; today, the .existence of ntl'aterrestrial intelligence is taken for granted by most scientists. Sir Bernard Lovell, one of the world's leading radio astronomers, has calculated that, even al lowing for a margin of error of 50003, ther~ must be in our own galaxy about 100 million stars which have planets ·of ·the right .chemistry, dimensions, and temperature to support organic evolution. If we consider that· our own galily, the Millty Way, is but one of at least a billion other galaxies similar to ours in the observable universe, the number of stars that could support some form of life is, to reach for a word, astronomical. As to advanced (by miserable earth standards) forms of life, Dr. Frank D. Drake of the National Radio Astronomy Observatory at Green Bank, West Virginia, has stated that, putting all our knowledge together, the number of civilizations which could have arisen by now is about one billion. The next question is, "Where is everybody?" The nearest neighbor to our solar system is Alpha Centauri, oniy 4.3 light years away; but, according to Dr. Su-Shu Huang of the National - Aeronautics and Space Administration, its planetary system is probably toci young for the emergence of life. Two other heavenly friends, Epsilon Eridani and Tau Ceti, about 11 light years away, are stronger contenders for harboring life. ::N~vertheless, if superior civilizations are abundant, the nearest would probably be at le:ist 100 light years away; therefore, it would take 200 years for a reply to be forthcoming, a small matter of seven generations. This should, J;iow ever, make little difference to us, in view of the enormous pofential gain from our contact with a superior civilization. · Unless we're terribly conceited (a very unscientific demeanor}, we must assume that the "others" are far more advanced than we are: Even a.50-year gap would be tremendous; a 500:year gap.staggers the imagination, and as _

1 The substance or this article was p~nted at a panel discussion of the same tide during the 1205 IEEE Conference on Military Electronics held in Washington, D. C., on 23 ~te::iber 1965. :&!sides the ~uthor as cryptologist, the other i:nemb!rs of the panel were Dr. Paul Garvin, linguist; Dr. John C. Lilly, delpbinologi.lt; Dr. William 0. Da'l:is; • . ph)"Sic:ist; and Fr. Francis J. Heyden. S. J., astronomer•.. The ~ts>r. v.-as Dr. Haroid Wooster, Director of Information Services of the Air Force Offic:e of Scientific Research. . - - .

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. . . UNCL~SSIFIED .. E_XTRATERRESTRIAL INTELLIGENCE · · . · . L. D. CAJ : - ···for~ ~~~o-;~·~ap·. ~·~ : ·~~·~e· way, ~·tiie;· ~--~ '~~~-:~.. ~ y~,---~- · . between; when these signals are a· , is behind us, forget it!) . ·It quite possible that '.'others'.' have satellite . .· ~'!ould·~~w :· . prhydrogen which permeates space to write out the message in raster m great clouds; moreover, this frequency is within the ranO'e of in 31 lines of 41 bits each; the latt£· radio frequencies able to pass through the earth's atmosphere . ., Pre ness in the patterns disclosed, in ~uma?ly, the_ significance of this frequency would be known to other din1ensions. In Fig. 2 is the writ i~~ellige~t th~ beings in universe who understand radio theory. We're binary l's have been replaced by a s~1ll ~bo~t _talking radio waves as the communication medium; other Now for its interpretation. possible media might be masers; lasers, or the as.yet undiscovered and There are dots at the four co1 unnamed "rasers." A .technology superior to ours might even have points, marking the outlines of th lea~ed how to modulate a beam of neutrinos (weightless. uncharged representation of the sun;. direct!:. pa~les that p~ysicists on earth find it difficult even to detect)· if so ~build representing 8 planets, identified l "they" may have to wait a century or two before we learn how their left, preceded by a binary r a neutrino receiver. legged beings illustrated are obvit If another civilization were teying to establish communication with hand of the male figure points tc, us, it would first embark on attention-getting signals of such a nature parcntly reside. At the top of th· that we could distinguish them from random cosmic noise· once we und~tanding tions of hydrogen, carbon, and receive a recognizable signal, v.•e have a good chance of chemical structure of life on their the message. For example, they could start with trains of simals corr~~ponding third planet there emerges a wa"Y to the natural numbers 1, 2, 3, ••• , followed perhaps water; the representation of a fish: b_y prime numbers. They might continue with equal-length extended _ apd the~(o.re have space travel. · ---sil,'!lals··cansisting of start and ~op-Impulses, "With occasional pulsts in · ··· to a i;ix (preceded by the usual c 2 In this con..,ection, Professor IC>fif Shklo\·sky, Russia's greatest radio astronomer there. are six fingers on each har r.as the iollov.ing to say in the September 1965 issue of Sooiet Liic . ' their number system is probabh• i • ·•Profo~nd crises lie in wait ror a developin: chilization and ane of them may well prove female figure may be seen a bracke ratal. Weare alreaciy familiar with several such critical (situatiaas}: . binary form (preceded by a binar: (a) ~~-destructiolf'as"a l'e51;11t oC a thennoaudear catastrophe or ane CKi.r disan"er1 . . wruch may have unpredictable and uncontrollable~ are 11 units high. A reasonable ~: g=:=oe·~~~-:·:_ ... · ·:_· .·· ...·.:·:. :: :: ... -.-:~~---~,~ -.-:.~··.-.--~~- --~ :i-:!:i~~~:!~~e~::t~:;: czcemi~ ~ar,;. • (d_) Restri_"cted. capacity of the indivi4\Jal's brain which rm lwl to ....-- · :· ....:...... ·· -·· ·. · ·--· · I n· 1952·· the B n"tish. math emat:. · · tion. WI th consequent danc_as of degeneration. . . •. (e) A crisis precipitated by the creation of artificial intellipnt beinp.;. address before the British Interpk or First Steps in Celestial Syntax.

UNCLASSIFIED 80

·- ":'··-·~ ...... -· .. .· IAL INTELLIGENCE · '· .. ·. .··- . . L. D. CALLIMAHOS ·. UNCLASSIFIED

J, if they are as much as 50 years be~ween; .'iible that "others" have satellite when these signals are aligned fiush over one another, they · :iem" anything that sounds non--- .. ~-- would show a circle, the Pythagorean Theorem,· or similar geometric . ave ·probably .Called us several -. ·- design. : These attention-getting signals ..would be followed by early for an answer; "or worse yet, they . "language lessons.~· interspersed with .it.em$ of technical information to · ey ha ve-i'eached such impressive · ...... help bring us up to the level of our superiorS, "them.". ; . . . . . - ~ destroyed.th.emselves. z .':: . ,_;::;. :...:·.: /: ·< .. ,.It. may be assumed .that the sense of sight~ .ot an- eqUivalent~ is ·.the .targetS on ·whlCh Dr.' Drak~·· ·· · -~ · . ·~- possessed by all higher forms of life; the problems of communication ~ of · 1960 in Project oZma, .an - ·. could thus be greatly Simplified through the medium of a "raster" signals from outer space. The representation such as that of a televisjon_~een. After a conference :s 1420.405752 megacycles per held at Green Bank in 1961 to discuss the possi"bility of communication This particular frequency, pos with other planets, one of the paz:ticipants, Bernard M. Oliver, made ;sors on the faculty of Cornell up a hypothetical message on the raste.r principle. The message, .ilip l\tiorrison, happens to be the consisting of 12'Zl binary.digits or "bits," is shown in Fig. 1. Since .. hydrogen which permeates space 1271 has but. two prime facto:rs, 31 and 41, we would naturally be led quency is within the range of to write out the message in raster form, in 41 lines of 31 bits each, or h the earth's atmosphere. Pre in 31 lineS of 41 bits each; the latter case reveals a greater nonranCiom uency would be known to other ness in the patterns disclosed, indicating that these are the correct .inderstand radio theory. We're dimensions. In Fig. 2 is the write-out of the message, in which the ? communication medium; other binary 1 's have been replaced by a dot and the O's left as blank spaces. '• or the as yet undiscovered and Now for its interpretation. 9erior to ours might e\•en have There are dots at the four comers of the pictogram as reference leutrinos (weightless, uncharged points, marking the outlines of the rectan~le. At the upper left is a it difficult even to detect); if so, representation of. the sun; directly underneath in a column are dots :wo before we learn how to build representing 8 planets, identified by the appropriate binary coding to their left, preceded _by a bimu-y point as a marker-~· · The erect, two o establish communication with legged beirigs illustrated are ob,,iously__ bisexual and mammalian; one -getting signals of such a nature ~and_ of the male figure points to the· fourth planet where they ap random cosmic noise; once we parenily reside. ·At the top of the pictogram may be seen representa- a good chance of understanding tions of hydrogen, carbon, and oxygen atoms, indicating that the lld start with trains of signals chemical structure of life on their planet is similar to ou.::s. From the 1, 2, 3, ... , followed perhaps third planet there emerges a wavy line, showing that it is covered with :nue with equal-length extended water; the representation of a fish shows that they must have visited us ;:iulses, with occasional pulses in and therefore have space travel. One hand of the female figul'.e points to a~ (preceded by the usual binary point), perhaps implying that l.:y, Russia's :;reatest radio astronomer, there are six fingers on each hand; we could therefore assume that ".le of Souiel Life: their number system is probably to the base 12. At the right of the ::li::ation 2J1d one of them may well prove female figure may be seen a bracket, in the middle of which is eleven in critical [situation.o;J: · - -- - binary form (preceded by a binary point}: this imphes that the oeings · ~--- -:ar c:itastrophe or some other di.!co\"ery :ollabi~ consecjuences. . are 11 units high. A reasonable interpretation is that the unit is 21 cm .• the wave length of the transmission, making them about 7 !-:? feet tall, which should be all right for ~verage Martians. ~ speciali~ :i which lead to exces.sh·e In 1952 the British mathematician Lancelot Hogben delivered ~ :on. address before the British Interplanetary Society entitled "Astraglossa, lcial intelligent beings." · or F~ Steps in Celestial Syntll.'~ Hogben pointed out that number . . .. . ~· 81 · .. · UNCLASSIFIED'.

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....•: . . L. D. c,. UNCLASSIFIED EXTRATERRESTRIAL INTELLIGENCE ..

. ~ . lOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO is tlie. most universal concept for . lOOOOlllOOO~O~OOOOlOOOOOlOOOOOOlOOOOOlOO 0000010001000000000000000000000000000000 intelligent beings; there!ore, mat! 00000010.0010~001000000100000000000010000 -~uooooo10001000001~000001000000001000100 steps in ematerrestrial com,muni 0100000001110000000000000010000000000001 · :::::.Cejuld transmit pulses representin 000000000000000000•000000000000~00000000 . l bs" tin" 0000000000000000000000001000001000000100 "rad1og yp represen g "+,, 0001000011000100000000001100000000000000 later carried out the basic idea : 0000000000000000000110000110000110000110 110ll0ll0100ll00001100101100101100100l00 shapes to represent elementary 10010010010101001001~0001100001100001100 different approach was developec 0 0 l 1 0 0 0-0 l l··O 0 0 O·O·O 0 (t 0 1 0 0 0 0 o·o 0 0 0 0 0 1 i. 1 1 1 0 1 0 0 0000000000000000000100000000000100000100 Mathematics at the University • 0000000001011011100100000000000001111101 0000000000000000000000000000100000000000 book entitled "Lincas: Design of 0000001000100111000000000000101000000000 "Lincos," an acronym of "lingu~. 0000001010010000110010101110010100000000 0000000101001000010000000000100100000000 munication of ideas through syro 0000000001001000001000000000001111100000 of those who have taken the trou 0000000011111000000111010100000010101000 0000000010101000000010000000000010001010 is too difficult. After all, the o· 0000000010100010000000000000000001000100 lOOOl000100llOllOOlllOllOll0100000100010 across to another party, whose 00101c1010001000100000000000000000010001 different from our own. In othe 0001001~0100010001oooooc1000000000000111 0000011111000001110000000111110100000101 an "inverse cryptography," or 0100000101000001000100000010000000000100 designed, not to hide meaning, I· 0001000011100001000001000001000000000010 0000100010001000100000100000110001100001 prehend. Clevern~ on ~he par-. 000001coo10001ooolooooolOOOOOllOOOOOOOOl 1000001101100011011000001100111 factor not reliance on ingenu crypt;grapher-somehow, this ti make his meaning clear to the r possess a cosmic equivalent of th€ o· As an illustration of how much & 0 e • minimum of material, and as an e~ G let us consider a message I have O• • • • 6 •e e.xpect of an initial co~~ical • shown a series of· transm.lSSlons v • • inhabited planet, many light y~ . • oec 0 ee• • ••• • •e••••. •• •· are representations for the 32 dit .• 0 e 11 •• oe •• •• •• or distinctive pulse shapes) heard . • • ••••• 0 --·The punctuation marks are no~ p· .eee .• -·· •...... -... - • ••• different time lapses: adjacent s: • • o eee· G e e e o •· unit) between them; a space be· e e Gfte e • • e • •· {2 units); commas, semicolons, an e e e • •· · 16 units ·respectively. Bet"'·ee1 . cie o e ee6eo ••••• •· . . . • • •• •e • •• • •• •.. • reference purposes) there is a tim • 0 • • ...... -- ••••. The first tr~ion, (1), is - ~ e e ••e• •--• different symbols _which will be t· .... • • • • • • • • • ••• •• •••• •••••• • •• ••• • •• mission (2) is the. clear implicatil • •• . ·- . •• a The Rosetta Stone is a piece or blac . . . ····•. ·- ·- ... . . • • . . . . . •• of the Nile. beanng a bilingual Wc:ription ·• • •• • • • • ••e· Fran~is C~ ·•-. ....•• .: . ••...... •• •e •• •• . and Greek) with which Jean Egyptian hieroglyphs. Fig. 2. UNCLASSIFIED 82

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UAL INTELLIGENCE L~ D. CALLIMAHOS . UNCLASSIFIED

)0000000000000000000 ~0001000000100000100 is the most universal concept for establisbizig communication between 30-000000000000000000 . intelligent beings; therefore, mathema~cs forms the basis for the .first . ·. ' )0100000000000010000 JOOOlOOOOOOOOlOOOlOO . steps in extraterrestrial communicatiaa·:.. He then illustrated how he ...... )0000010000000000001 l 0 0 0 0 0 0 0 0 0 o-o 0 0 0 0 O"(f"o 0- could transmit pulses representing integerS. "and distinCtive .sigri.aIS or . . . . ·-- ) 000 l._O_O O O O l O O O O O O l O O "radioglyphs" representing"+'~.... _ .., "=:='!,·and so on. -.-Mo~on JOOOllOOOOOOOOOOOOOO further~-USing 100001~0000110000110~ -later:carried out the basic idea. a little different pulse·. . ... > o 1 o 1 1 o:~ l -o 1 1 o. o l o o l o o - shapes to represent elementarY ·mathematical s}'mbols.·- ·An entirely . • o o o 1~ o o o o 1100001100 · _ •OOOO-VOOOOOlllllOlOO different approach was developed by Haris "Freudenthal, Professor of ' .0000000000100000100 )0000000000001111101 Mathematics at the University -of Utrecbtt-who in 1960 published a '0000000100000000000 book entitled "Lincos: Design of a Language for Cos."'llic Intercourse." 0000000101000000000 .0101110010100000000 "Lincos," an acronym of "lingua cosmica," tries to establish a com- ·0000000100100000000 .munication of ideas through symbolic logic, but the general consensus 0000000001111100000 101010000001010~000 of those who have taken the trouble to study his book is that his :Plan- - 0000000000010001010 0000000000001000100 is too difficult. After all, the object of the exercise is getting ideas 0110110100000100010 across to another party, whose thinking processes may be ef!tirely 0000000000000010001 0001000000000000111 different from our own. In other words, what we need to develop is 0000111110100000101 an "inverse cryptography," or communication symbolism specially 0000010000000000100 1000001000000000010 designed, not to hide meaning, but to be as easy as possible to com 0100000110001100001 0010000011000000001 prehend. Cleverness on the part of the sender is then the important 0001100111 factor, not reliance on ingenuity of the recipient. The inverse cryptographer-somehow, this term doesn't sound quite right-must make his meaning clear tO the recipient, even if the latter does not possess a cosmic equivalent of the Rosetta Stone.3 As an illustration of how.much information could be conveyed with a minimum of material, and as an example of facile inverse cryptography, let us consider a message I have de\.ised to be typical of what we might I. ~pect of an initial communication from outer space. In Fig.· 3 is shown a series of ~..nsmissions which could have come from another inhabited planet, many light years away. The 32 arbitrary symbols are representations for the ~2 different signals (combinations of beeps, or distinctive pulse shapes) heard on a frequency of 1420.4 megacycles. The punctuation marks are not part of the message, but here represent different time lapses: adjacent symbols are sent with a short pause (1 unit) between them; a space between symbols means a longer pause (2 units); commas, semicolons, and periods indicate pauses of 4, 8, and 16 units, respectively. Between tr'allsmiS-Sions (numbered here for ref~re.!lce p~) there is a time lapse of 32 units. The fust tram;rni$sion, (1), is obviously an enumeration of the 32 different symbols which will be used in the communications; in trans mission (2) is the clear implication that A represents the integer 1, B - . . ' The Rosetta Stone is a piece of black basalt fCIUlld. m 1799 near the Rosetta mouth . of the Nile. bearinc a bilingual inicription cm ECYJ)tiaD. hieroglyphics. Egypaau demotic. and Greek) with which Jean F~ Clwnpollioo was able to solve the mystery of the Egyptian hieroglyphs. ,·. -~. . -~ - ·. -.. .· . UNCLASSIFIED

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L. D. CALLIMAHOS UNCLASSIFIED UNCLASSIFIED. EXTRATERRF.

Ill .A. B. C. D. £. F. C. H. -l· .J. X. L. II. X. O. P. Q. 11. S. T. U. T. W. X. T. Z. the integer 2, ••• , J the integer •. &.. S. c. #. @. A. B. C. D. E. F. C. H. I. J. L L. K. II. II. P. Q. It. theie~are introduced symbols !Qr S. T. U. T. _W. %. T • .Z•• !~ &.. S. c. #. @. in teaching. us their mathemat .::: .. ··121 A A, B: A A A. C; A A .& .\, D: A 4 A A A. £; 4 A .l .l .& I.. F; .l .l .l A .& A A. C; A A .l A A A A A. H; .l A .l .l .l A A .l .l, I; .l A A A A & 4 A .l .l; J. addition, subtraction, multiplic: 13) A K A L B; .l IC A X A L C; A It A 1( A X A L D. .l It A. L B; B X A. L C: C X .A L D. · ~ and the concept of zero; fuequa B X C L £; E LB It C; F X D L J; J L DIC F. E L X £; XE LE.· roots; and definitions of ...- and (.Cl C Jl A. L B; D JI A L C; C II E L B; E II C L II a. new to the 31 symbols recoverec ISi D IC Ir L D; C IC Ii L C; F II: F L II; E 11 E L Ir. most beautiful concepts in pure (6) J L .AH; J X .A L .AA; J K i L A.I; AA X A L A.I. J K J L Ill; J It J X J L CK; 1H x c··i:. ic: · - - - · • · - · · if they can teach us. suCh a·com··

(7) B 0 C L F; D 0 B L H; E 0 B L AM; D 0 All L ll!f. be staggered by what they will (8) F P C L B; H P B L·D: J P B L E; J P E L B. transmission. Beginning with (9) .A P J L Q J; A P .AHN L Q ANH; Q J. P J L Q AXIi. cluster concepts are introduce• (10) Q J L R 4: Q J 0 B L II B: A II E II A. L It E L E 0 Q J. Q A..'111 L 11 KA; transmission (30), we now are u: Q .lHlf 0 B L It N!I. pure Venerean. Furthermore, Ill) H L H; C S C. C S C. · D IC A L C Ii: B; D X C S E X A; E IC A S D X C. the code they are using on us 1121 D T A; D T B; D T C; D L D; D U £: D U F; D U C. J T !: J U AA. thousands upon thousands of (13) F'IP.II V CN; .A.'i!il!I K C Y ~; A.'1 P C Y ale. this is easily appreciated by an. 11.CI W£KA.XLEXCBWEXAXL11BOEXX11BOAXLiO~ the meaning of all 30 transmissic llSI c T i L !; E y B L BE; a T E L ca; .. D K A x T !I L !E. Even right after this first mes· 116) 3£ Z B LE; ;;) Z BL H; IC Z CL C; .ASE Z CLE. WAI X F X;:: BL E. • EE ?. B_L.• 11 £~ JI .\!!: Z C L 11 E. .IE Z B L 10! £. with that planet, we shall have< (17) D • L D 0 C 0 B 0 A }.. BD; £ • L E 0 D 0 C 0 I 0 A. L .Ailf; H • L DllC!ll. Fermat's Last Theorem, Golc

(18) &. P D L 4 II Q C X Q E II Q C X Q I It. &. Y CKADJ.EI. unsolved problems in mathem:

S L A X Q W A • X X Q 11 B • I Ii: Q 11 C • X X Q ll" D • X X. S Y ECA.'flH. not be difficult for "them" to c <. 1201 c E K A # L I' E It A X; B c E IC .A # L B I' E K 4 X; nological superiority (first of B r £ ~ ll" D X C X # L B 11 E: K C X. c B i c D I L I" I X 1' :> X L i 0 D. . . able to call us!). If "they" b· 1211 S r c &. 0 11 II A X Z B # K A L 11. structure constant," they are at 122) B K C L c @1'"IO.I. #: B X C L £. C 0 D L c @h"!U. #: C 0 D L :.a. five for sure, su.spect the sixth, D ! !I L • @li!IA #: D r a L ~- ratio, among others, of the spel 1:31 ii K C L £: c @);Id #. B IC D L E; c @!INC #. E Y I L IE; c @lilll #. F T I L C £; electron; it may take a century c @NNC #. I T E: c @liU #. H U C; c @ lillC #. &. Y B!QiGH; c @llllC #. And after we re5olve our pre." (24) 5 L c @h"!ID #. C L c @>GIQ #. E, C. AA. AC. AC, c 4ilillll #. AIL\ c @llllD #. appropriate to. make discreet 1251 c @llHE # L B D &. c @A I: c @hllF # L &. c @.I. # T I. c @'A # L c @lllC f. c @Hh"E # L B &. c @!INC #: c @NMF # L &. c @llllC # T I. . harmony and peace with our re: 126) c @i.1i!f I L D o Q c O &. c @~ I r c. othenvise ingested by the Stli 1%71 Q B X Q D IC Q H It C! AF X Q C!I. Y A: fortune to contact us. But as Q 5 K Q D IC Q !! X Q ltF K Q CB I< c" @lllfl # L .&. (and generations of his descend: 128) C .Y. c @A IL C; c @.& # L D •• ·l Kc @.l # L .AB; c @A IL C. i"i> Z c @.A # L H; c @A # L I. c ~A i L .A, It C::. II il CC. J P C, &.. £, 11. c @li!II #. • The solution may be found on p. l c @I # L A. II C::, II It CC. J P C, &.. IC. II, c @llNI p. • \Y-dh what he haS learned fro.tr c @C # L A, lt C::, II It C::. J P c. &., IC, 11. t @llllt #. reader formula~ these two questions_d . 1291 c @llllE r L I l c @a #: t @llH7 # L &. c @I p r I. compact Corm; the solutions appear on c @JWI # L B c @C # l[ B t @D #:.. c @llAA # 1. c @C I O t @D #. classic umolved problems in mathemati {30) c @NH£ # L c @HAI #; c @X. #: t @lllCF I L c @MAD #, c @IW: #. values ol z. y, and z can be found c @!WI.. # 1. c @HAI I_. c @ui: #: c @JW. # 1. c @IWI #. c.@IW: f. is an intepr peater than 2; Goldbach's other mathematicians Wied to make t: Fi(.3. number greater than 2 can be expn.ssed

UNCLASSIFIED 84 UNCLASSIFIED

.: ••.• p .: . •• : .. . : ' ...... :· . .· ... .· ··~ .. ·...... :.. ·... · .. :: ...... ~ ...... , .. .~·:r··· ~~-· '·• t . .. .. : -,,_}.,, ...: .. ,_...... ,._ ...... ·.-.··....-...-....,.;• ';_,_..;,..__;.,,,:_,.. ______.. _::_·_'·-·- .... ----· .. ··-·-·-···-

:.IM AH OS UNCLASSIFIED UNCLASSIFIED ·EXTRATERRESTRIAL INTELLIGENCE

~- O. P. Q. It. S. T. U. V. W. X. T. Z. the integer 2, •.• , J the integer 10. In .the first twenty transmissions r. c. H. I. J. x. L. JI. II. 0. P. Q. a. there are introduced symbols !Qr the· introductory expository treatment • E; l l l l l l, F: l l l l l l l. C; in teaching us their p:iathematics~ Among the items treated are: I: J.. l A·.\ A A l A A :J.: ·.J. ·- addition, subtraction, multiplication~ and division; ·decimal notafion · · · · · · • L D. m L B; B K .\ L C: C It A L D. and the coneept of zero; inequalities and apprg.rimation; po~ers and K F. E L K E: X £ L E. ·. -·..-- roots; and definitions 'll' and e: . Transmission (21) adds nothing . L II B. of to the. 31 symbols recover~4 t}lu5 far, but it does quote o,ne of the L H. new most beautiful concepts in pure mathematics: they are telling us that, . L il. J X J L Ill: J K J X J L Cll; if they can teach us suCh a complex notion£ this early stage, we will 'f L l!!I. be staggered by what they will teach us by the 200th or the 2000th ;:. s. transmission. Beginning with ·transmission (22), words and word :. Q A.'111. cluster concepts are introduced, so that by the time we come to C: L E 0 Q J. Q Alilf L It HA: traniinission (30), we now are understandiiig~· m·a-maimer of Speaking, - . pure Venerean. Furthermore, we can now see how we could recover ,c C S E It A; E X .L S D K C. the code they are using on us, and which will obviously consist of P'; D U C. J T I: J U I.A. thousands upon thousands of code groups with different meanings; :c. this is easily appreciated by anyone who takes the trouble to fathom ;: X K I B 0 J. X L '!I 0 F. the meaning of all 30 transmissions in the foregoing example.• : AX 'I'll L 5£.

Z C l. !:. Ir Al X i' X Z B L E. Even right after this first message, if we are in direct communication -~::. with that planet, we shall have questions to put to "them": the prooi of cc.a 0 AL A!li; H • L Dh'CIH. Fermat's Last Theorem, Golcibach's conjecture,£ and many ocher unsolved problems in mathematics and the natural sciences. It wiil X !; Q lr D • X K. S V l!!'J:A.'lil!. not be difficult for "them" to demonstrate their intellectual and tech : E ;.: A. X: nological superiority (first of all, don't forget it was they who were ;. t i) i L 1' !I X lr D X L ll 0 D. able to call tis!). · If "they" but know the secenth digit of the .. fine ·structure constant," they are ages ahead of us {we know only the first five for sure, suspect the sixth). 'l'his number, 137.039 ... , is the ratio, among others, of the speed of light to the speed of the hydrogen : ~- !: ! a L !!:; • @llNB 1- r T B L c £: ~ :.~•= i. ' v ?:"--:;.;.'i..'ltl: c·@·1111c ;. electron; it may take a century to calculate this constant to 9 d:gits. :.C. ~. • @ll.~'D #. A!IA t @!IND -J. And after we resolve our pressfrig scientific questions, it might be . c €•A j. Y ll. r '!PA # L c @llNC j. appropriate to make discreet inquiries as to how we could live in ~ c ~>::: ; ?' 8 .. harmony a.11d peace \\ith our fellow man-that is, if we aren't eaten or otherwise ingested by the superior civilization that had the good fortune to contact us. But as far as the cryptologist is concerned, he his i L AB: t @A i L C. (and generations of descendants who might experience the supreme

~: l""I§/ h'!I? /.. - • Tliesolution may bi: rciUndOii p.'109;-bui tiie {. c ~NKI P. esci:iew ?rematiire Piek. ·· ;, c @IQII F. s \\1th what he has teamed Crom this example of space communication, let the

1§3 ~ Y B. reader formulate these two questions dinctly for t.-.insinimon to "them." in a clea= and >A # L c ~C i 0 c @D #. compact form; the solutions appear on pg. 109. For the reader who is a little rusty on classic unsoh-ed problems in mathematics, Fermat's Last Theorem stares that no integ?'lll i L c @lil.:I i. c @~Ci. _-;. L c 'f•$AO #. c @~_#. ,,·aJues of z, y, and z can be found to satisfy the equation r' + Y' • ;;• , if n iS an integer peater than 2; GcMdblch's "?IOtorious" c:onjec:tme ("notorious" only because other mathemaci~ failed to make the conjecture themselves) states that every even number pater~ 2 can be a:pn:ssed as tbe sum of two primes.

UNCLASSIFIED- . UNCLASSJFIED .. ... ; " ~ ·.r. • .· ...... : ·..,. . •;. - . _:·;.··;: ·" ··;: ·.. -··: ...... ·:· ..._ .. : -· .·.·...... : ;

L. D. CALLIMAHOS UNCLASSIFIED -ainn of their lives when we hear from ..them") must keep a level head, not- g:et excited, and be- prepared to cope with problems the like of .:..Wliich ~e has never seen-:out of tlUs world, so to speak. Electroni( -~· BY JOHN Topt:: INTRODUCTION Calligraphy, the art of prodc familiar term in the English Ian~ letters in its alphabet, English r manual or mechanical. Slight· tions have little effect on legib tei.-ts are easily obtained due to P.Jl that is necessary is a ucique ~ it is a typewriter key or .:? cor: English requires only that a sig1 · letter. The Morse and Baudot sult of.such transmissions is ~ Generally speaking, most alp; graphic problems. However, s< graphic in nature. Such langu: sent some idea or thing. Althc rules of formation, the number often very large. For exampl• thousand unique ideographs. I1 as a single element. The followi lar symbolc; with very dissimilar r

Character -'1-A- -.------··-···- ~"' ------71------ .If ------ ~ ------

Therefore, ,for these languages, tention in order to obtain intelli . 86 UNCLAS$1AED .! ,; .! .-. i .. ,-~.,_..,,... :_""":'~~7".' _ __,,...... ,...... ,..I""'!'-....,._."'!·. ·'"'· :""' ••·."""·;- .. '. P. -•,; >:-n<: ';' ,- -...... :- .. , ..

60!

.. .. . -· ·- -- -··-·

Symbols A 1 I 9 Q reciprocal Y power ·B 2 J 10 R decimal point z.. root c 3 K+ s ;.:£ factorial D4 L == T > & -:: E 5 M- u < s e F 6 N 0 v == (: [ G 7 0 x W{ # ] HS p ....,... x) @code Code values 001 qi;estion 007 radius 013 circle 002 true 008 volume or sphere 014 area 003 false 009 ... (ellipsis) 015 recta.,gle 004 prime 010 perimeter of rect. 005 circum. of circle 011 area of rectangle 006 area of circle 012 perimeter 999 Code values 1, 2, 3 ... 99 - x, y, z . . . {abstractions, unknowns, variab~es).

Fermat's Last Theorem: . ------··- ¢@A # Y c@ D # Kc@ B # Y c@ D # L c@C # Y c@ D : . c@ D # L B; ¢ @NNB #. c@D # L C, D, E, c @ NNI ~; c@NNB NNA:.

Golciliich's Conjecture: -·-.a.-· B c@A-#. Bc@A # L¢@B #; c@B #TB~ t@B # Lc@C # Kt@D #; ¢@C "# Le@N:t:m #,t@D # L¢@NND _:. ¢@NNB NNA #. . ··.l .-

- . . - . . ·uo!+-e:>FCIDtIIttIO:) ao-eds ,soqsUX!lI'eJ ·iw-01 ao~n1<>s . - . :

s:oN.ao I'I'!aI.NI 'lVI'li.LSSffii::CJ.vCLLXa 031:HSSV1)N0

' I • .. ·.~,.-:..: •• ._ -"'·-:·'~ .>-__ .._._., ..•••/~·--.:.-~.:.;.c;.:.::·· .. ? ·• . .'"; •.. ·-!""'·'"""~ ...... :.,,,.· ..: ~ . .· .:"" ..·