ICARUS41, 178--192 (1980)
Mutual Strategy of Search for CETI Call Signals P. V. M A K O V E T S K I I Institute of Aviation Instrument Manufacture, Ulitsa Herzena, 67, Leningrad 190000, USSR
Received December 12, 1978; revised September 10, 1979
A strategy of search for call signals from extraterrestrial intelligence (ETI) is suggested, assuming a mutual desire to communicate. Angular convergence leads to the principle of natural beacons--the directions to the most conspicuous objects of the Universe. On the time axis convergence leads to synchronization of transmission by the observed occurrence of Nova (Supernova). Every star receives according to a schedule of the first contact with every other star. An example of a schedule is given, stimulated by Nova Cygni 1975. The schedule conception imposes heavy demands on the precision of astrometry. Fixed and statistical components of the schedule are considered. A small angular vicinity of Nova Cygni 1975 is a potential source of signals from ETI during the next 20-40 years. The Earth must transmit call signals on the day of observation of maximum Nova outburst toward the stars located within a small angular vicinity of the direction antipodal to the Nova. A systematic analysis allows the, removal from call signals of the most dangerous anthropomorphisms: the type of modulation, the rate of transmssion, the codes (languages). It leads to physicomathematical call signals in the form of a product of the physical constant, fH, and mathematical ones (or, 2¢r, 2 ~/z, l/or . . . . ). The precision in the received frequency, ~rfH, of monochromatic oscillation is the criterion of intelligence.
INTRODUCTION
CONVERGENCE APPROACH
The existence or absence of extraterrestrial i n t e l l i g e n c e ( E T I ) c a n n o t b e p r o v e n b y any speculative arguments. Recourse s h o u l d b e m a d e to o b s e r v a t i o n s a n d s e a r c h . At present, there are three methods of s e a r c h f o r E T I : a s t r o p h y s i c a l ( s e a r c h for thermodynamic and information wastes of the ETI's activity), communicative (search for C E T I ' s signals), a n d t h e s e a r c h for Bracewell probes. This paper deals with the communicative method. An ETI of Earthlike l e v e l o f d e v e l o p m e n t o r s o m e w h a t h i g h e r will b e a s s u m e d as t h e o b j e c t o f search. The present author believes that extremely developed ETIs, possessing the Galaxy, are impossible for many reasons ( M a k o v e t s k i i et al., 1979). It will a l s o b e a s s u m e d t h a t t h e E T I s o u g h t f o r is willing t o c o m e into c o n t a c t .
The communication seeker should search f o r t h e signals s e n t b y E T I to o t h e r E T I s . He searches for a major property of the o b j e c t s o u g h t f o r - - i t s i n t e l l i g e n c e , its willi n g n e s s to c o m e into c o n t a c t . T h e intellig e n t c r e a t u r e , t r a n s m i t t i n g signals, n a t u rally w i s h e s t h e s e signals to b e r e c e i v e d a n d r e c o g n i z e d , a n d t h e r e c e i v i n g side und e r s t a n d s this w i s h a n d , in t u r n , s t r i v e s for t h e s a m e goal. T h e m u t u a l g o a l f o r b o t h sides is t h e m a i n c h a r a c t e r i s t i c o f t h e c o m m u n i c a t i v e m e t h o d a n d is l a c k i n g in ordinary astrophysics. T h e p r o b l e m o f C E T I is v e r y i n t r i c a t e s i n c e it m u s t b e s o l v e d u n d e r c o n d i t i o n s o f complete lack of a priori information on the site o f E T I ' s t r a n s m i t t e r a n d t h e p a r a m e t e r s o f its signals. T h e s p a c e o f s e a r c h f o r E T I ' s signals is, in g e n e r a l , t e n - d i m e n s i o n a l : 178
0019-1035/80/020178-15502.00/0 Copyright © 1980 by Academic Press, Inc., All rights of reproduction in any form reserved,
CETI--MUTUAL STRATEGY apart from the four-dimensional physical subspace (R, or, 8, t), determining the coordinates o f the ETI sought for, there is a sixdimensional information subspace (f, m, b, r, c, s). Unknown are the frequency f, the kind of modulation m, the width of the spectrum b, the rate of transmitting the information r, the code c, and the semantics of the communication s. Thus, H = II(R, ct,
~ , t , f , m , b , r , c , s ) . (1)
Consecutive scanning of all the points of this ten-dimensional space is practically impossible, and this fact is understood not only on Earth but by all the ETIs as well. Therefore, both transmitting and receiving ETIs will try to reduce the a priori uncertainty. Each ETI striving for contact has the problem of reducing a ten-dimensional space to a point, single and universal, or, if impossible, to a finite number of points. The selection of a single point in the search space implies the optimization of the communication line throughout all its parameters. The understanding of this difficulty and the necessity to overcome it cause all the ETIs to search for and find the only key parameters accessible in their common "ecological niche," the Galaxy; its phenomena, characteristics, dimensions. The Galaxy's matter provides each side with a certain set of parameters. The task of each side is to choose independently the same parameters on each of the axes of search space, to read correctly "the instructions of the designer general." The major tool needed to achieve this is a conscious mutual drawing together (convergence) of two intelligences, solving a single problem in a single ecological niche. Biological evolution has transformed the shape of the dolphin into the streamlined shape of a fish. Convergence has resulted in the same "constructive" solutions. The common ecological niche has proved to be " t h e designer general": the dolphin's shape converges not with the fish's shape but with that streamlined shape which is dictated to
179
both dolphin and fish by the environment and by their function. The means of convergence is a spectrum of possibilities provided by a set of mutations and the vitality of a mutation leading the species in a proper direction. The convergence of intelligence repeats the biological convergence. It also presupposes (a) the presence of demand for drawing closer together, (b) the possibility of variations, and (c) the ability for selection. The only difference lies in the fact that natural selection (c') of the most favorable mutation is entirely objective while artificial selection (c") of the communication line contains certain elements of subjectivity. A well-known example of a convergence selection is the traditional rendezvous "under the clock" by two persons having no a priori information about the point of rendezvous, but having a priori information on the "ecological niche" containing the point of rendezvous, and expecting the partner to have the same information (as well as his demand for rendezvous). The procedure of selecting the place of rendezvous and statistical results are considered by Makovetskii (1976c, p. 414). G. Cocconi and Morrison (1959) were the first to apply this concept to the problem of CETI. Their selection of the range of communication waves and the concrete frequency of communication ("under the clock" of neutral hydrogen, fu --- 1420 MHz) is a typical convergence procedure. In the present paper the author summarizes his attempts (Makovetskii, 1973, 1976a,b,c, 1977a,b,c, 1978a,b, 1979, etc.) to extend the procedure of Cocconi and Morrison to cover all the dimensions of the search space. The problem is first solved for call signals, i.e., signals whose only function is reliable testimony to the artificiality of their source. MUTUAL ANGULAR CONVERGENCE
Mutual convergence toward the conspicuous delta function fH on the frequency axis
180
P . V . MAKOVETSKII
is aimed at an increase in the probability of contact. With this in mind we will consider the possibility of using the most conspicuous delta functions on the axes ~, & L e t us begin with a model o f the Galaxy having no conspicuous directions, Let the Galaxy be h o m o g e n e o u s , spherical, and contain an infinite n u m b e r of stars with finite distances between them. All the stars are Sun-like, N of them are within the range of radiocommunication, n of N having c o m m u n i c a b l e intelligences, but a priori information on directions toward E T I is lacking. In such a galaxy there is nothing on which to fix a direction and the direction of search is indifferent, c o n v e r g e n c e is impossible; each E T I has no alternative but to search throughout t h e s p h e r e . L e t each E T I have one transmitter and one receiver working (at a proper frequency). The probability that at a given instant the E a r t h ' s b e a m is directed toward one of the E T I s is equal to Pl = (n - 1 ) / ( N -
1)-~ n / N ;
(2)
the probability that the radio b e a m of this E T I at a given instance is directed toward the Earth, is equal to P2 = 1 I N .
(3)
The probability of contact at a given instant (the time of E T I is reduced to that of the Earth) is Px = PiPe =
n / N 2.
(4)
The mean time of search before the first contact is T~., = r / 2 p k
= NZr/2n,
(5)
where r is the time of recognition of the contact event. Let the model of the Galaxy be modified by introducing into it a very conspicuous astrophysical object, the Crab, for example. There appears a center of attention, an organizing (for intelligence) principle. The Crab is being studied; therefore the direction toward the Crab, in o n e ' s mind, appears to stand out sharply and it b e c o m e s a
stimulus for mutual convergence. Thus not only the Crab, as an astrophysical object, is introduced into the Galaxy but also a certain cognitative structure, consisting of n straight lines passing through the Crab and e v e r y ETI. In this structure the Crab performs the function of a natural beacon; it is a delta function on the surface (a, 8). The civilizations located on different sides of the Crab, on a straight line passing through the Crab, b e c o m e cognizant that the telescope of any of t h e m probably keeps in its field of vision the telescope of the other side. It implies that for t h e m the search for E T I in the direction (a, 8) is already mutually accomplished. The perception of this fact by both partners is the major step in the c o n v e r g e n c e of their thinking toward a conscious use of the Crab as a beacon for contacts, i.e., toward switching on the transmitter and receiver of C E T I ' s call signals. This step is nonanthrop o m o r p h o u s to the degree that are the concepts o f direction in space, of conspicuousness of an astrophysical object, and of willingness for contact are. It is readily perceived that if both E T I s are on one side o f the Crab, then one o f them must send call signals in a direction antipodal to the Crab. An a priori unawareness m a k e s the Crab and its antipodal point equivalent natural beacons. The c o n c e p t of beacons is purely convergent: the efficiency o f the b e a c o n method is not due to the fact that on a r a n d o m straight line Earth b e a c o n there are s o m e w a y or another, more civilizations than on another, but is due to the fact that these civilizations, if existing, regularly and consciously send their call signals toward the beacon more frequently (Makovetskii, 1978a). It is equally easy to perceive that the probability for two E T I s to fall on one straight line with the Crab is negligible. H e n c e , E T I s will transmit (receive) within a certain cone with its center in the Crab. I f the angular dimension of this cone is equal, for e x a m p l e to one degree square, then the n u m b e r of stars in the cone M =- N/41,253
CETI--MUTUAL STRATEGY and the n u m b e r of civilizations m = n/41,253. I f the search is to be carried out in this cone only, then the mean time until the first contact is analogous to (2), Tk2 = M Z r / 2 m
= Tkl/41,253.
(6)
This very large gain is the major advantage o f the b e a c o n concept. The gain, however, is obtained at the expense o f reducing the n u m b e r o f civilizations with which we can c o m e into contact, from n to m. The structure of contacts in the Galaxy proves to be radial (with its center in the Crab). Each E T I can c o m e into contact only with those located on the straight line E T I Crab. I f E T I s are rare, then, probably, for certain receivers m < I, and then their contacts by means o f the Crab are impossible. The n u m b e r of contacts can be increased if several b e a c o n s are used: s u p e r g i a n t s , globular and scattered clusters, pulsars, large cepheides, the center o f the Galaxy, the m o s t conspicuous extragalactic objects (M-31, M-33). Taking, for e x a m p l e , 100 beacons (and 100 antipodes), we obtain a 200-fold increase in the n u m b e r of civilizations and the same a m o u n t o f decrease in, the efficiency of the b e a c o n conception: Tk3 = (200M)2z/2.200 m = 200 T-kz---- Tkl/200.
(7)
Specification o f an object as a beacon is to s o m e degree a n t h r o p o m o r p h i c (due to the c o n c e p t o f conspicuousness). T h e r e is no doubt, h o w e v e r , that a considerable n u m b e r o f b e a c o n s will be specified by both sides identically. It is this fact that makes the strategy o f b e a c o n s valid. We have discussed the c o m m u n i c a t i v e c o m p o n e n t of the strategy of angular search. It is evident that in the real Galaxy the astrophysical considerations (spectrum o f a star, possessing s o m e planets, etc) should also be taken into account. The most correct strategy is a combination o f astrophysical and c o m m u n i c a t i v e strategies: in the cone, catered by a given beacon, the first to be tested are the stars m o s t promising for the p r e s e n c e of E T I .
181
MUTUAL CONVERGENCE OVER DISTANCE It is evident that there are c o m m u n i c a tive stimuli to begin the search with the nearest stars (R --~ min): a dialogue m a y be started with E T I ; we can do with a transmitter o f lower p o w e r and a reception antenna o f smaller area; the a priori information on Doppler shift in the communication channel is m o r e accurate; etc. The convergence argument lies in the fact that all the a b o v e factors are objective and therefore k n o w n to both sides. Astrophysical arguments do not coincide with those of communication: civilizations are conceived not at the stars nearest to Earth but at Sun-like ones, probably. Nevertheless, a Cen and other nearby stars, whose astrophysical arguments for search are small (but not equal to zero) are to be tested for the p r e s e n c e of signals due to be presence of powerful c o m m u n i c a t i v e and c o n v e r g e n c e stimuli. MUTUAL CONVERGENCE OVER TIME For communication operators the time axis is s y m m e t r i c about that of frequency: to search at the instant tree 4: ttr is as unreasonable as searching at the frequency free 4: ftr (here, tree and free are the instant and frequency o f reception, /tr and ftr are the instant o f arrival and frequency o f the signal being transmitted to Earth). Just as it is considered logical on the frequency axis to bind transmission and reception to the most conspicuous f r e q u e n c y fH, SO it is expedient on the time axis to bind it to the most conspicuous event. The most conspicuous and distinctly fixed in time and space are such events as outbursts of s u p e r n o v a e and novae~ L e t us consider a current example. The Earth o b s e r v e d the m a x i m u m outburst o f N o v a Cygni at the instant to = August 30, 1975. I f all E T I s , observing this N o v a and having adopted the c o n c e p t of synchronization, switched on their transmitters at the instant they o b s e r v e d the m a x i m u m outburst, then the Earth (and other ETIs)
182
P. V. MAKOVETSKII
~
o f all 10~ stars entering into the schedule annually. The problem o f improving the accuracy of measuring interstellar distances by two to three orders of magnitude becomes rather urgent. Nevertheless, there is a possibility of examining annually about 9 × l04 stars even without accurate astrometry (Makovetskii, 1979). The geometric spot of all ETIs whose signals reach the Earth at moment to + t is the ellipsoid of revolution;
OVO
I 11 No~o~
1
/
\x. x
~1
/I
\/
R, + R
\
FIG. 1. Synchronization of CETI call signals by Nova outburst. The broken line Novat-ETIi-Earth differs little from the straight line Nova,-Earth; therefore ETI call signals are late but few with respect to the outburst observation on the Earth. The ETI2signal arrives later, simultaneously with ETI3and all ETIs on the ellipsoid surface. Nova3 has had an outburst recently, and the ellipsoid relevant to it is very narrow at the present instant. could determine (Fig. 1) the date of arrival of call signals by the formula to + t = August 30, 1975 + R, + R - R0,
(8)
where R, + R is the length of the broken line N o v a - E T I - E a r t h , R0 is the distance N o v a - E a r t h (all R are given in light years). For nearby stars R ~ R0 (=5000 light years) and then t ~-- R(1 - cos /z),
(9)
where/x is the angular distance between the N o v a and the star being tested for the presence of ETI. As an example, a schedule for several stars is presented in Table I (Makovetskii, 1976b,c, 1977a). The spectrum of the star and its binarity are neglected since we do not know with certainty their role in the formation of ETI. The potential accuracy of the method makes up a few hours (accuracy of fixing the maximum outburst). The actual accuracy for the Earth due to Earth's poor astrometry is at present sufficiently lower and does not permit effective examination
- R 0 = t = const,
in whose foci the N o v a and the Earth are located (Fig. 1). The ellipsoid's semiaxes are the functions of time a = c +t/2;
b = [ct +
t2/4] '/2,
(10)
where c = R o / 2 = 2500 light years (L.Y.). During the first 100 years after the observation o f outburst, t ~ c, and then ct - c;
b =- (ct) "2.
(11)
T o d a y (t = 4 years) we have a = 2500 and b - 100 L.Y. The volume of ellipsoid E, (Fig. 2b), from whose surface at a given instant the signals begin to reach the Earth, is V,
=
(12)
k T r a b 2 = ~Trc2t.
Let each ETI transmit call signals during r years (for example, ~- = 1/36.5 years = l0 days). Then the volume of ellipsoid E2, from whose surface at a given instant the signal ceases to reach Earth, is 4 b V2 = ~zrot(
Ab) z = krrc2(t -
z).
(13)
The volume of the " m e l o n peel" between ellipsoids E, and E2, wherein all ETIs are located, and whose signals have already started to reach the Earth and have not yet ceased, is V = V,-
V2 =.~rrce~" = 7 × I0"~(L.Y.) 3.
(14)
Assuming the star density within the ellipsoid to be constant and equal to one star by 8 parsec a - 250 (L.Y.) 3, we find that
within this " m e l o n peel" there are perma-
C E T I - - M U T U A L STRATEGY
183
TABLE I SCHEDULE OF FIRSTCONTACTSOF CETI STIMULATEDBY OUTBURSTOF NOVA CVGNt, AUGUST30, 1975 Woolley (1970) catalog
Other catalogs
R (light years)
/z angular distance)
to + t~ (date)
_+At, (days)
o
9723 9717A, B 820A, B 806 15A, B 860 802 9699 905 725A, B 34A, B 829 699 768 53 48 559A, B 35 411 65A, B 702A, B 71 144 280A, B
Ross 248 Struve 2398
80 68 11.1 38 11.55 12.9 44.5 64 10.3 11.5
I 2 9 6 12 14 8 8 25 24
15 54 38 02 02 12 24 43 35 23
Sept. 6, 1975 Sept. 30 Oct. 25 Nov. 15 Dec. 1 Jan. 23, 1976 Feb. 20 July 5 Sept. 2 Sept. 7
2 5 0.4 5 2 1.7 30 30 4 4
7/Cas Ross 775 Barnard's Star Altair Wolf 12 Ross 318 a Cen van Maanen's Lalande 21185 UVCet 70 Oph r Cet ~ Eri Procyon
17.9 21.8 5.98 16.5 25.5 28.5 4.39 13.6 8.2 8.88 18.7 11.8 10.8 11.33
32 30 60 40 36 34 134 62 92 88 60 88 100 122
56 48 10 39 20 47 17 41 02 45 46 01 35 45
July 15, 1978 Aug. 25 Sept. 2 Aug. 25, 1979 Aug. 20, 1980 Oct. 5 Dec. 25, 1982 Jan. 5, 1983 Mar. 15, 1984 Apr. 20 Mar. 20, 1985 Jan. 15, 1987 June 15, 1988 Feb. 25, 1993
23 30 5 30 40 70 25 35 30 60 80 70 45 90
61 Cyg Grb 34 Kruger 60 Wolf 1084
n e n t l y 2600 stars, e n t i r e l y r e n e w e d w i t h i n 10 days. T h e p o s i t i o n o f the E a r t h w i t h i n the ellipsoid is s h a r p l y e c c e n t r i c ; t h e r e f o r e the d i s t a n t h a l f o f the " m e l o n p e e l " is proj e c t e d for the o b s e r v e r o n a v e r y small a n g u l a r a r e a in the N o v a ' s v i c i n i t y . Its a n g u l a r d i a m e t e r (Fig. 2b) 2/z0 -- 2 arc
tg(b/c)
-~ 2 arc
tg(t/c) 112,
(15)
a n d t o d a y (t = 4 years) it is e q u a l to 4036 '. W i t h i n this circle t h e r e exist daily 1300 p o t e n t i a l call signals, a n d w i t h i n a circle o f d i a m e t e r 8°, t h e r e are 2300, i.e., - 9 0 % o f the w h o l e c a p a c i t y o f the s c h e d u l e . T h e d e n s i t y m a x i m u m o f call signals is o f circular s h a p e , c o n c e n t r i c with N o v a C y g n i , at a n a n g u l a r d i s t a n c e f r o m it e q u a l to 1°22 ' ( c u r v e 4 in Fig. 2a). A t a m a x i m u m the
p o t e n t i a l d e n s i t y o f call signals is e q u a l to 105 stars per s q u a r e degree. A c c o r d i n g to (15), this m a x i m u m s l o w l y s p r e a d s in the c o u r s e o f time. I n Fig. 2a, c u r v e 1 c o r r e s p o n d s to t = 1 ( A u g u s t 1976), c u r v e 20 - t = 20 ( A u g u s t 1995). T h e s c h e d u l e p r e d i c t i n g the date o f arrival o f signal from e a c h star i n d i v i d u a l l y ( T a b l e I) m a y be r e f e r r e d to as d e t e r m i n e d (it is d e t e r m i n a t e l y a s s o c i a t e d with the outburst of N o v a and R , a and 6 of ETI). Then the d a t a o f Fig. 2a m a y be r e f e r r e d to as a statistical c o m p o n e n t o f the s c h e d u l e . T h e r e is n o n e e d for a s t r o m e t r i c d a t a ( R , a, 6), s i n c e the s e a r c h is c o n d u c t e d n o t b y a n i n d i v i d u a l star b u t o v e r the c o n t i n u u m o f the " m e l o n p e e l . " T h e d i s t a n c e e r r o r o f the o r d e r o f 20% distorts b u t little the o p t i m u m a r e a o f s e a r c h o v e r the angle. T h e d i s t a n c e to E T I m a y be m e a s u r e d b y the date o f
184
P. V. MAKOVETSKII n,
stars/sq, deqree
3I o
i
~
arth
FIG. 2. Schedule statistical component. The ETIs whose signals arrive at the Earth today are between ellipsoids EL and E2. The position of the observer is sharply eccentric; therefore the distant half ABD is projected on the area of the celestial sphere around the Nova with a small angular diameter, 2p,o. The angular density of potential call signals (a) depends on angular distance from the Nova (it) and on time elapsed after burst observation (curves for I, 4, and 20 years). Continuous search should be made for 20--40 years with a sharply directed beam within 2p,o. arrival o f its call signals t~, by the direction of the signal's arrival a, 6, and by R0 (and now, after contact, the a c c u r a c y R0 bec o m e s actual). U n d e r conditions of p o o r terrestrial ast r o m e t r y the statistical c o m p o n e n t is much m o r e important than the determined one (Makovetskii, 1977a). The statistical component exists continuously and for a long time (decades). In addition, the stars of this c o m p o n e n t are nearer to the N o v a (2-10 times) than to the Earth. That is why for these the luminosity o f N o v a is 4-100 times brighter and it is the strongest stimulus on which to switch the transmitter. The disadvantages of the statistical schedule are also substantial. The distance to most of its stars is 1000 < R < 5000 L.Y. ; therefore the signals from their E T I s are
104-10 ~ times w e a k e r than those from the nearby stars in Table I. The search o v e r the continuum takes into account the Doppler shift of frequency with respect to the local standard o f rest but it disregards the individuality of the star's motion. That is why the required range of search is b r o a d e r than when working on an individual star. These disadvantages can be s u r m o u n t e d by using an antenna of large aperture and precision wide-band spectrum analyzer of the cyclops type (Sagan, 1973a). For N o v a outbursts 10 times nearer than N o v a Cygni, the statistical schedule will be 100 times smaller, and the n u m b e r of transmitters per degree square will be reduced 1000 times (determined schedule is almost independent of R0). Therefore, the opportunity provided by the outburst of N o v a Cygni should not be lost. The following are the advantages of this strategy of schedule. 1. An infinite wait for call signals from a particular star is substituted for a fixed point on the time axis. This saves the operative time of the telescopes both transmitting and receiving. 2. Transmission according to the schedule reduces the p o w e r c o n s u m p t i o n thousands of times. 3. The method is simple: the c h a n g e o v e r to operation by the schedule requires no expense. 4. The method is universal: in principle it includes the entire Galaxy, and in particular cases (/.~ ~ 0), a part of other galaxies as well (Makovetskii, 1977a). 5. The method is precise: its potential accuracy is about a half day. Its practical a c c u r a c y will increase along with progress in astrometry. The limited a c c u r a c y for E a r t h is a particular case. More a d v a n c e d E T I s have already m e a s u r e d the Galaxy with far greater accuracy; that is why the schedule's capacity is m u c h higher to them. T o join the club o f civilizations, an advanced a s t r o m e t r y is probably an indispensable threshold, a level of d e v e l o p m e n t the E a r t h has not yet reached.
CETI--MUTUAL STRATEGY 6. The method contracts astronomical time to that of the human being: at small/.,, t~R. 7. The method is unambiguous: it converges toward one synchronizing signal only (the light o f Nova). At the same time it is compatible with any signals being synchronized (radio, laser, etc.) whose propagation velocity is known. 8. The concept o f synchronization is nonanthropomorphic. It is understandable to any ETI that understands the concept of time. 9. The concept of synchronization is invariant with respect to technology as well as to linguistic, physical, and mathematical languages. 10. The accuracy o f synchronization is an independent criterion of artificiality: a signal of any kind, received strictly at an instant predictable only by the hypothesis of synchronization, i.e., artificiality, supports this and only this hypothesis. 11. The synchronization principle is absolute: under no advance o f ETI will it be outdated; neither will it b e c o m e u s e l e s s because the more highly civilized the ETI, the more it appreciates the saving o f time and effort (barbarism decreases). 12. The smaller the number o f ETIs in the Galaxy belonging to our communication horizon (Sagan, 1973b), the more difficult it is to establish contact " a t least with anyb o d y , " and the higher the danger of premature loss o f interest in contacts (pessimism), the higher the value of the synchronization principle, facilitating and accelerating the contact, making the search time reasonable and, therefore, more optimistic and resultative. 13. The synchronization system may be used as an intercivilization astrometric complex permitting the difference between the predicted and the true instants of arrival o f call signals to refine the gridwork o f distances between ETIs. 14. The high probability of the schedule (due to a complete convergence) permits, ill the absence of signal, the tentative conclu-
185
sion that this particular star is ETI free which is supported further by e v e r y nova to which the star does not respond. Convergence toward the schedule concept has already taken place on Earth: independently o f Makovetskii (1976b,c, 1977a) the concept o f synchronization by Supernovae came to Tang (1976), and the concept o f schedule of N o v a Cygni 1975, to McLaughlin (1977). This is a strong psychological argument to the effect that the schedule concept will come into the minds o f other ETIs. If not, then the value of the schedule concept would be equal to zero. The same is true with respect to the concept o f Cocconi and Morrison (1959). STRATEGY OF TRANSMISSION The Earth must transmit call signals if it expects to receive transmission from others. The transmitter begins to transmit at the instant he observes the N o v a ' s maximum outburst (practically, apparently, a few hours later, since the position of the maximum on the time axis is determined post factum). It would seem that since our aim is to achieve a maximum n u m b e r o f bilateral contacts for Earth, the latter should transmit call signals toward all the stars contained within the ellipsoid (Fig. l) from where we expect to receive signals. However, such a strategy is erroneous. Although a signal from ETI star 9723 (see Table I) is delayed with respect to the outburst of N o v a only 7 _+ 2 days, our signal (had we transmitted it on August 30, 1975) would reach it t =R(1-
cos /z) ~ 2R = 160 _+ 30 years later,
(16)
after the observation o f the N o v a Cygni outburst by star 9723. (We assume the identical accuracy o f astrometry both for the Earth and for ETI-9723.) The practical benefit of such an inaccurate prediction (16) is negligible and, therefore, ETI-9723 will not expect a signal from the Earth. Conse-
186
P. V. MAKOVETSKII
quently, there is no reason for the Earth to transmit a signal toward ETI-9723 within the schedule of N o v a Cygni. The contact will not b e c o m e bilateral; it will remain unilateral (9723 ~ Earth), what is in essence a semicontact. Most of the stars in Table I h a v e / z < 90 °, i.e., the E T I s of these stars transmit signals at the angle /z' > 90 ° with respect to N o v a Cygni. The statistical part of the schedule also operates only on the assumption that all the E T I transmitters emit almost strictly antipodally toward N o v a . It is evident that the Earth must also o b e y this requirement, imposed on us by astrophysics, geometry, and the principle o f causality: we must emit antipodally to Cyg, i.e., toward Vel (Makovetskii, 1977a). By doing so we shall provide a m a x i m u m n u m b e r o f semicontacts for these E T I s which keep the Earth in either the determininistic or the statistical part of the schedule. This is a very peculiar detail in the strategy of first contacts: we should not try to achieve the m a x i m u m n u m b e r of bilateral contacts for the Earth. Such an individualistic strategy will not be supported by the E T I s applying the schedule concept. We should try to achieve a m a x i m u m n u m b e r of semicontacts for the Galaxy as a whole (collectivistic strategy). I f all E T I s strive toward this aim, then a m a x i m u m n u m b e r of bilateral contacts per one civilization on the average will be attained in the final analysis. For instance, it is more reasonable to transmit a signal toward ETI-9723 in the future, at a p r o p e r instant, having waited until an almost antipodal outburst of N o v a Vel, which will take place in 50 years, on the average, and will provide a very accurate schedule for a semicontact, Earth --0 9723. E a c h ellipsoid of reception is very well catered for by N o v a , , Nova2, Nova3, etc., contained in it (Fig. 1). Figure 3 d e m o n s t r a t e s the strategy of transmission. Let ellipsoid E with a N o v a and the Earth' in its foci be the region from where the Earth receives signals by the schedule during, e.g., T~e~ = 10 years after
observation of the outburst. This limiting ellipsoid is a geometric locus of points for which R~ = var and but R1 + Rrec = const, R ~ + R r e c - R 0 = const = Tree= 10.
Rre c = v a r ,
(17)
For ETIrec R0 = var, Rtr = var (for different transmitters); R~ = const. Then its ellipsoid o f reception is R 0 + Rtr-
R~ =
10,
or
Ro + Rtr = const = R~ + 10.
(18)
F o r the transmitting Earth, R~ = var, var (different receivers). Then, according to (18),
Rtr =
R~)- Rtr = const = R~ - 10.
(19)
This is the limiting hyperboloid of revolution H with N o v a and the Earth in its foci. Hence, the surface, embracing all E T I s expecting signals f r o m Earth not longer than 10 years by the schedule of N o v a Cygni 1975, is the hyperboloid of revolution, confocal with the ellipsoid of reception by the same schedule. The angle between the axis and the a s y m p t o t i c cone o f the hyperboloid (Fig. 3) is c = 3o27 '. To b e a m the whole continuum at such a wide angle is noneconomical. It is m o r e reasonable to b e a m either with a discrete sharp b e a m each star in turn or all the stars simultaneously with m a n y discrete b e a m s (in each of which the field intensity is proportional to the distance Rtri as far as the ith star). The envelope of the whole set of b e a m s is the hyperboloid mentioned above. It should be noted finally that the distribution of beacons and outbursts of N o v a e o v e r the celestial sphere has its m a x i m u m on the galactic equator, i.e., just where the m a x i m u m n u m b e r of E T I s are located. This is in good agreement with the requirement for maximization of the n u m b e r of contacts. SYSTEM A N A L Y S I S A N D S Y N T H E S I S OF CALL SIGNALS
Following the suggestion by Cocconi and Morrison (1959) on the selection of fre-
CETI--MUTUAL STRATEGY
I
] I ~'I~,RI +Rmc = consl =
.ll/l ~"~arth ==s,o
II "/;
o
.o-,O
#' '2!2 beams
FIG. 3. Time-angular strategy of transmitting call signals from the Earth. Reception of call signals: from within ellipsoid E, corresponding to R1 + R r e e = R0 + I0. Transmission of call signals: antipodal to the Nova, into hyperboloid H, corresponding to R'0 - R t r = R 0 10. Transmission toward every star i with a sharply directed beam (intensity of field in the beam is proportional to R t r i ) . q u e n c y f = fH for c o m m u n i c a t i o n with E T I , a n u m b e r o f attempts have been made for analogous selection o f the most conspicuous values for m , b, r, c, and s (see, e.g., Dixon, 1973; Sagan, 1973a). The optimization, however, was conducted for each of the p a r a m e t e r s separately, rather than as a general case of transmission o f information. An attempt is made in this section to ref r a m e the p r o b l e m o f call signals in terms of s y s t e m analysis in which the whole s y s t e m o f variables in c o m m o n is subjected to optimization. L e t us consider the variables included in the s y s t e m (f, m , b, r, c, s). The first of these, f , is a physical object; the subsequent m , b, and r are technical ones; c, linguistic; s, semantic. Thus, in the information subspace the call signals are synthesized from objects belonging to four different areas of knowledge: I~mo d =
physics + technology + language + semantics.
(20)
The reception and deciphering of call signals will be successful only on the condi-
187
tion that the set of concepts in a particular area of knowledge, both ours and E T I ' s , intersect and the c o n c e p t being used lies on the intersection. Physics investigates an objective reali t y - t h e Universe, one for all. Undoubtedly, elements such as galaxy, star, supernova, globular cluster o f stars, hydrogen, oscillation, sinusoid, frequency, and m a n y others lie on the intersection o f two kinds of astrophysics. Unlike physics, natural p h e n o m e n a technology describes the products o f civilization not originating in nature. T h e s e products bear the imprint of a historic progress of civilization, apparently, to a large degree of an individual nature. Therefore, to assume that E T I ' s technology repeats ours in such details as the amplitude or width-pulse modulation is an obvious anthropocentrism. O f even greater uncertainty are such technical p a r a m e t e r s as r and b. All this is quite valid with respect to codes (languages) whose diversity is inexhaustible. Languages, as the products o f two different civilizations, which have not yet c o m e into contact, differ from each other still more than material implements of production. The area of intersection of semantics of two civilizations cannot be identified before contact (we do not k n o w the history, physiology, esthetics of E T I , etc). Only about the intersection in such divisions of semantics as m a t h e m a t i c s can we speak more or less confidently. On the primary elements, rigidly fixed to objective reality (natural series o f numbers, the value o f zr, addition and multiplication operations, etc), two kinds of mathematics intersect almost reliably. Thus, the class o f call signals employing modulation and codes is e x t r e m e l y anthropocentric. I f E T I understands this as well, it will design call signals by the formula excluding technology and languages (Makovetskii, 1973, 1976a): II,M = physics + mathematics.
(21)
188
P.V. MAKOVETSKII
It is this formula that possesses a minim u m of a n t h r o p o m o r p h i s m (m, b, r, and c are removed) and m a k e s it possible to establish contacts with all the E T I s with which we can find mutual understanding today. The call signals, described by formula (21) will be referred to as modulation free or physicomathematical. Specifying formula (3) a new class of call signals m a y be suggested
contains. Determination of the n u m b e r of correct signs is nothing but determination of the precision of fabrication of the signal by technology alien to us, the unfamiliar system of calculation. But we can analyze it in our s y s t e m of calculation with our instruments, in our own language. Substitution of the signal by a product of this kind is put forward here not for the first time. One hundred and fifty years ago Carl Gauss suggested terrestrial "call signals" II,M = 4)VM, (22) for the Martians: a vast rectangular triangle where 4) and M are the physical and mathe- of forest with squares of wheat fields along matical constants; V is the simplest mathe- its sides (Sullivan, 1964). This illustration of matical operation--multiplication ( x ) or di- the Pythagorean theorem m a y also be revision (+). As the first example of garded not as a signal but as a demonstramodulation-free call signals we consider tion possessing the same advantages as rrfn. The Gauss call signals, as well as n'fu, II,M = rrfH differ f r o m modulation call signals by the = 4,462,336,274.9288(53) Hz. (23) fact that they bypass the a n t h r o p o m o r H e r e the criterion intelligence is the pres- phism o f technology, languages, and partly ence of the irrational cofactor ¢r by which the theory of knowledge, i.e., the most nature cannot multiply f r e q u e n c y f n without dangerous reefs of the C E T I problem. intelligence's participation. If, having reThe call signals, 7rfH, are not the only ceived a purely sinusoidal oscillation of possibility in the class 4)VM. H o w e v e r , a frequency H,.x~ and dividing this frequency careful convergence analysis allows selecby the familiar frequency of hydrogen (Tay- tion on a two-dimensional plane, p h y s i c s lor e t al., 1969) mathematics, a very limited n u m b e r of the m o s t popular points of r e n d e z v o u s with fH = 1,420,405,751.7864(17) Hz, (24) E T I . Thus, e.g., the frequency fn has wellwe can see that the resuJt of division is 7r; k n o w n advantages a m o n g 4). These are the more correct signs we have in the listed in detail by Dixon (1973). These adresult, the m o r e reliable the testimony to vantages are so n u m e r o u s and evident that the intelligence of signal II,xl. the probability o f using fn m a y be considIt should be noted that in current infor- ered to be substantially greater than the mation theory the call signals of one 7rfu~ probability for foil, fmo, and others. Due to type are not considered as a signal: modula- this fact a c o n v e r g e n c e of two intellects tion and codes are lacking, the spectrum arises: everything that is evidently less reliwidth and the rate of information transmis- able is neglected. sion are equal to zero. The sinusoidal oscilIt is more difficult to make the same lation of frequency rrfH m a y be considered definite selection for M as for 4). After a as a physical object, directed toward us careful selection (Makovetskii, 1976a,c, p. from E T I for recognition as a product of 421) three nearly equivalent constants reintelligence (like a spaceship or a TV set). main Unlike an ordinary signal, the more deterM = or, 27r, 2 w'. (25) minate and m o n o c h r o m a t i c the call signals 4)VM, the more reliable the establishment of The present author believes that constant contact (more correct signs), i.e., the more 7r is known to all E T I s capable of making semantic information this m o n o c h r o m e contact with us. Thus the most reliable
CETI--MUTUAL STRATEGY frequencies of the "call make" are n~, M = 7rfH,
2rrfH, frt2 l/z,
fn/Tr, fn/27r, fH/2 ''2. (26) These six points on the frequency axis, as we expect, will be used simultaneously. The suggested class of modulation-free call signals has many advantages (Makovetskii, 1973, 1976a, 1978a): 1. The absence of modulation (m, b, r) and codes (c) reduces the dimensionality of the information subspace of call signals from 6 to 2. 2. The two-dimensional subspace, frequency-semantics, by selecting frequency fH and semantics in the form of cofactor zr (or 2zr, 2 ~/2, 1/zr . . . . ) is reduced to a few fixed points. 3. The operation for deciphering of sense is substituted by that of measuring--a universal one. 4. Frequency is to be measured--the only parameter, the one to which the measurement of most values in modern metrology is reduced (terrestrial and, probably, ETI). 5. The reception and "deciphering" of call signals may be started from any instant of transmission (in case of modulation, only at the beginning). 6. Call signals are invariant to the technique of the sender, to his physical (quantum wave) and mathematical (system of calculus) languages (bear no traces of the latter). 7. The absence of modulation eliminates the necessity for detection, commonly bringing about losses at small signal-tonoise ratio. 8. Monochromaticity permits a filter of very narrow bandwidth and increases the range of operation. 9. The information of a monochromatic signal is not distorted by dispersion in the interstellar medium, unlike the information of a wide-bandwidth signal. 10. Multiplication off~ by 7r, 21t2. . . . . shifts frequency to the portion of the range
189
free, both from emission and from adsorption in interstellar hydrogen. 11. Call signals of the zrfH type do not prevent fH from being used as a source of astrophysical information. 12. Call signals of the ZrfHtype indicate precisely the frequency sought. As a result, the necessity for search over frequency, in principle at least, is reduced. At frequency fH it was hampered by hydrogen emission, therefore Cocconi and Morrison (1959) suggested searching not at fH but "near fH" which may not be regarded as an accurate indication of frequency. 13. The proposed criterion of artificiality, i.e., the number of correct signs in the frequency received (irrationality of abstraction ~-) stands out sharply among the criteria proposed previously, mainly, astrophysical (Kardashev, 1964). 14. The artificiality criterion zr is compatible with other criteria of artificiality, i.e., monochromaticity (Troitskii, 1965) and schedule (see above). 15. Call signals of the zrfH type are compatible in time with other stages of communication (transmission of codes and scientific information), probably requiring modulation. In this case the part of call signals will be played by the carrier or the "center of mass" of the spectrum. The criterion of artificiality in this case as well is not distorted by the interstellar medium. Thus, the advantages of modulation-free call signals are rather diversified and attractive, a fact which enhances convergence toward them in many ETIs with various modes of thinking. CRITERION OF A R T I F I C I A L I T Y
The number of correct signs n,~ in the received value of frequency (23), testifying with assurance to the signal artificiality, depends on an a priori probability of ETI's presence in the beam. At present, however, this probability is extremely subjective. The problem is even more sophisticated: although nature cannot multiply frequency by an irrational factor, it can generate fre-
190
P.V. MAKOVETSKII
quency rrfH directly. " I n terms of philosophy nature can reproduce everything that is made by intelligent c r e a t u r e s " (Ambartsumian, 1965). As a matter of fact, in a continuous spectrum of radio noises the 7rfH frequency occurs on equal terms with its neighbors, meaning that the proposed criterion o f artificiality, as any other criterion of decision making, is statistical. When verifying any hypothesis (scientific, medical, or judicial; complex or elementary) the decision about its validity is made on the basis o f a finite number of experimental examinations. The judgment on sutficiency of a given, inevitably limited number of examinations (in this case the number of correct signs) is always purely intuitive (Feinberg, 1976). In this sense the new problem of detecting the ETI call signals differs in no way from any problem already involved in science experience. If we detect a certain frequency fl and dividing it by fn obtain 3.14, then we will recognize this cofactor as an approximate value o f Tr and that is why we will b e c o m e sharply cognizant of the extraordinariness of the event. This means that the subjective probability o f the hypothesis on contact with ETI becomes intuitively significant even at n~ = 3. By detecting three more correct signs, we will objectively increase this probability 1000 times (by 1000 times will be reduced the number o f unknown natural spectral lines capable o f competing, with regard to location, with the specified one). The main reasons that may restrict n~ are the signal/noise ratio and Doppler and gravitational shifts of frequency. The Doppler effect also determines the range of search over frequency. The signal/noise ratio, all other things being equal, in call signals of the 71"fn type, is best due to the foregoing advantages 7, 8, 9, 10. Other considerations are well known and will not be discussed here. If the Doppler effect is not compensated by both sides, then n~ = 4 is typical, which would be a poor criterion of artificiality. Compensation significantly increases n~
and, in addition, decreases the range of search. The methods to compensate the Doppler effect applicable to the problem of C E T I have been discussed by Dixon (1973) and Makovetskii (1977c). A method may be suggested that does not compensate the Doppler effect directly (does not reduce the range of search), but does radically increase the number of correct signs n~, eliminating the Doppler masking from the criterion of artificiality. This is a double-channel method, using two operative frequencies, e.g., lrfH and fH/Tr. The result will be free from Doppler and gravitational shifts. Moreover, from the ratio of frequencies, the cofactor f a vanishes (as well as its theoretical inaccuracies and technical instabilities), having accomplished its part as a guideline o v e r the range prescribed to it by Cocconi and Morrison (1959). By virtue of this, the accessible n= becomes theoretically unlimited. Practically, it will be limited because of the absence o f mutual correlation between the inner noises of the two receivers, but at a sutficiently prolonged observation n~ = 1315 can be obtained. Further increase in n~is limited due to inequality of fluctuations of the velocity of radiowave propagation at two frequencies (due to fluctuations of heterogeneities in the interstellar medium). The double channel method, unlike the Doppler compensation, does not exclude the necessity to search over frequency (within the limits of the Doppler uncertainty). In channel fH/~ this uncertainty is 7r2 times less and the first stage of search should be carried on in this channel, using the second one for making a decision on artificiality. 1 CONCLUSION Mutual convergence of two intelligences allows the following conclusions on search At the frequency of positronium,fp = 203 383 MHz (Kardashev, 1979) the range of search is 150 times greater than at frequency fn, which makes frequency fp less attractive.
C E T I - - M U T U A L STRATEGY
and transmission of ETI's call signals: 1. The probability of contact in the directions marked by natural beacons is substantially higher than in a random direction. 2. The instant of search is determined by a schedule of contacts, synchronized by outbursts of Novae and Supernovae. Today the determined schedule, synchronized by Nova Cygni 1975, is operating. 3. There is also a statistical schedule with daily participation of - 2 0 0 0 stars of potential ETIs, located in a small angular vicinity of Nova Cygni 1975, which should be continuously investigated during the next 20-40 years for call signals. 4. Very reliable call signals are nonmodulated code-free signals in the form of monochromatic oscillation at frequencies "rrfH, 2arfH, fH21/2, fH/Tr, fn/2*rfn/21/2. 5. The criterion of artificiality should be the accuracy of observing both frequency and schedule, as well as the degree of monochromaticity of oscillation. 6. The criterion of artificiality is free from Doppler masking if two or more of the above frequencies are received and their ratios are measured. 7. Transmission of call signals from the Earth should be started on the day of observing the maximum of a Nova's outburst. The direction of transmission is toward the stars near the point antipodal to the Nova. 8. The accuracy of the determined schedule is restricted to errors of the Earth's astrometry. Increased accuracy of astrometry is urgently needed. 9. The service of Novae and the precise recording of the instant of maximum outburst and distance to Nova are also significant. The particiation in searches by observers and also amateur astronomers is highly desirable. ACKNOWLEDGMENTS The author is indebted to V. A. Ambartsumian, N. L. Kaidanovsky, Yu.N. Pariisky, N. T. Petrovich, T. A. Rozet, M. A. Sokolov, and V. S. Troitskii for the interest in and support of the concepts presented, to
191
V. S. Makovetskaia for help in calculations, as well as to two anonymous reviewers for useful remarks.
REFERENCES AMBARTSUMIAN, V. A. (1965). In Symposium: Extraterrestrial Civilizations. Proceedings of the Conference, Buracan, 1964, p. 136. Acad. of Sciences, Armenian SSR. COCCONI, G., AND MORRISON, P. (1959). Searching f o r interstellar communications. Nature 184, 844-846. DIXON, R. S. (1973). A search strategy for finding extraterrestrial radio beacons. Icarus 20, 187-199. FEmaEaG, E. L. (1976). Art and cognition. Vop. Filos. N 7, 93. KARDASHEV, N. S. (1964). Transmission of information by extraterrestrial civilisation. Astron. Zh. 41, 282-287. KARDASHEV, N. S. (1979). Optimal wavelength region for communication with extraterrestrial intelligence: h = 1.5 mm. Nature 278, 28-29. MAKOVETSKII, P. V. (1973). Problem of first contact, V polet, N 21. Institute of Aviation Instrument Engineering, Leningrad. MAKOVETSKII, P. V. (1976a). Structure of call signals from extraterrestrial civilizations. Astron. Zh. 53, 221-224. MAKOVETSKII, P. V. (1976b). Call signals of extraterrestrial civilizations. In Proceedings of the Institute o f Aviation Instrument Engineering, Leningrad, May, Vol. 98, p. 137-139. MAKOVETSKll, P. V. (1976C). In Get at the Root? [Smotri v koren!], 3rd ed., p. 414. Nauka, Moscow. MAKOVETSKII, P. V. (1977a). Nova Cygni--a synchrosignal for ETI? Astron. Zh. 54, 449-451. MAKOVETSKII, P. V. (1977b). Reduction of uncertainty in search for ETI. Astron. Zh., in press. MAKOVETSKll, P. V. (1977c). Call signals of ETI zrfntype and Doppler effect. In Complex Radioelectronic Control Systems, Vol. 118, p. 150. LIAP, LETI, Leningrad. MAKOVETSKll, P. V. (1978a). Efficiency of relation of ETI call signals to natural phenomena. Radiofizika 21, 139-141. MAKOVETSKII, P. V. (1978b). Signals of ETI: What, where and when to Search? Znanie-sila N 8, 46. MAKOVETSKII, P. V. (1979). In Get at the Root? [Smotri v koren!] 4th ed., p. 353. Nauka, Moscow. MAKOVETSKII, P. V., PETROVlCH, N. T., AND TROITSKII, V. S. (1979). ETI-problem is the search problem. Vop. Filos. N 4, 47. MCLAUGHLIN, W. I. (1977). On the timing of an interstellar communication. Icarus 32, 464-470. SAGAN, C. (Ed.) (1973a). Communication with Extraterrestrial Intelligence (Symposium in Buracan, 1971). MIT Press, Cambridge, Mass. SAGAN, C. (1973b). On the detectivity of advanced galactic civilization. Icarus 19, 350-352.
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SULLIVAN, W. (1964). We Are Not Alone McGrawHill, New York. TANG, T. B. (1976). Supernovae as time markers in interstellar communication. J. Brit. lnterplanet. Soc. 29, (July-Aug). 469-470. TAYLOR, B. N., PARKER, W. N., AND LANGENBERG, D. N. (1969). The Fundamental Constants and Quantum Electrodynamics Academic Press, New York/London.
TROITSKII, V. S. (1965). Certain considerations on search for intelligent signals from universe. In Symposium: Extraterrestrial Civilisations. Proceedings of the Conference, Buracan, 1964, p. 97. Academy of Sciences, Armenian SSR. WOLLEY, R., EPPS, E. A., PENSTON, M. J., AND POCOCK, S. B. (1970). Catalogue o f Stars within Twenty-five Parsecs o f the Sun. Royal Observatory Annals, Sumfield & Day Limited, Eastbourne, Sussex.