herbie@watdcsu.UUCP (Herb Chong - DCS) (08/22/85)
>You're assuming there's only a few intelligent races in the galaxy. Besides: >why would a reace with a low exploratory/reproductive/etc. drive acquire >interstellar travel? And so what if they can survive for 1000 years on a >single solar system: that still leaves time for 3,000 iterations of the >explore/colonise/fill a solar system/explore cycle if they're only 1% >ahead of us. And do they have to fill the solar system before they want to >go for the next one? you're assuming there are many. maybe this will help somewhat. this is excerpted from a physics project of mine from many years back. this is not to say that one can't assume that there are many and go on from there to write a damned good SF novel, but one must account for the large number somehow if the story is to have a reasonable scientific basis. Herb Chong... I'm user-friendly -- I don't byte, I nybble.... UUCP: {decvax|utzoo|ihnp4|allegra|clyde}!watmath!water!watdcsu!herbie CSNET: herbie%watdcsu@waterloo.csnet ARPA: herbie%watdcsu%waterloo.csnet@csnet-relay.arpa NETNORTH, BITNET, EARN: herbie@watdcs, herbie@watdcsu --------------------------------------- extraterrestial communication "empty space is like a kingdom, and earth and sky are no more than a single individual person in that kingdom. upon one tree are many fruits, and in that one kingdom, many people. how unreasonable it would be to suppose that, besides the the earth an sky that which we can see, there are no other skies and no other earths." (Teng Mu, scholar of the Sung dynasty, c. 1000 AD) "[i have] a deep conviction and foreknowledge, that ere long all human beings of this globe, as one, will turn their eyes to the firmament above, with feelings of love and reverence, thrilled by the glad news: 'brethen! we have discovered a message from another world, unknown and remote. it reads: one...two...three...'." (Nikola Tesla, Jan. 7, 1900) "those who feel that the goal justifies the great amount of effort required will continue to carry on this research, sustained by the possibility that, sometime in the future, perhaps a hundred years from now, or perhaps next week, the search will be successful." (Frank Drake, 1960, radio astronomer who was first to seriously try -- unsuccessfully -- to detect signals from intelligent extraterrestials) 1) how hard is it to find another intelligent life form that we can talk to? no successful systematic search for other intelligent life can be made if we don't look far enough out into the galaxy away from us. how far we have to look depends upon how many there are out there listening for other intelligent life like us. for the moment, let us assume that there are N stars with planets in the galaxy which currently have intelligent life capable of interstellar communication. let N_star be the total number of stars in the galaxy. the ratio N/N_star, which we will define to be p, gives the probability that any single star is currently supporting intelligent life capable of communicating with us. the probability of examining exactly k stars before finding one such planet is given by p(1-p)^(k-1), the familiar geometric distribution. the average number of stars that must be examined to find one can be easily shown (by using the definition of the mean of a discrete random variable) to be 1/p. to be 50 per cent sure of finding a planet for a given value of p, the smallest value of k where the cumulative distribution sums to greater than or equal to 0.50 represents the average number of stars that have to be examined. a little manipulation of the infinite sum of the pdf gives a value for k at this critical point, k_50 = ln(2)/p. following are values of k_50 for various values of p. p k_50 10^-2 70 10^-4 7000 10^-5 70,000 (Sagan) 10^-6 700,000 1/3*10^-6 2,000,000 (von Hoener) 10^-8 70,000,000 if we assume the local density of stars, rho_star = 10^-3/ly^3, is constant for an appreciable distance away from us, the volume of space that must be examined is given by V = n/rho_star. for Sagan's estimate, V = 7*10^7 ly^3 while for von Hoerner's estimate, V = 2*10^9 ly^3. assuming that a sphere of radius r enclosing this volume is an appropriate shape, r is approximately equal to (V/4)^(1/3), or 260 and 790 light years respectively for Sagan's and von Hoerner's estimates. to be 90 per cent sure of finding a star system containing a planet with intelligent life that can communicate with us, the radii are 390 ly and 1200 ly respectively. these distances from Earth are still within the spiral arm that the sun is a part of so the stellar density is approximately constant. the stars that look the most promising for finding life similar to our own are the familiar G3 stars very much like the Sun and other types that are spectrally similar. 2) how many extraterrestial intelligences are there out there? the following equation has been proposed by many astronomers to estimate the number of intelligent civilizations in the galaxy that are capable of communicating with us. N = R_star f_p n_e f_e f_i f_c L the different terms in this product vary in reliability from relatively precisely known to wild speculation. the terms are defined as follows: R_star: rate of star formation in the galaxy - about 10/yr assuming it has been constant since the beginning of the universe f_p: fraction of stars with planets - still debated, but may be as high as 0.40 n_e: fraction of planetary systems capable of supporting life - no consensus, why not use our's as an example, 0.2 f_e: fraction of planets capable of and developing life - speculation, be optimistic, say 0.3 f_i: fraction of planets with life that develops into intelligent life - more speculation, 0.3 f_c: fraction of intelligent life capable of communications - your guess is as good as mine, 0.1 L: average lifetime of such a civilization - be optimistic, 10,000 yrs using these numbers, we get N = 72 in our galaxy at this time, so that p is about 10^-8 and V and r are about 10^11 ly^3 and 3000 ly respectively. a total of 10^8 stars need to be examined to be 50% sure of finding one that harbors an intelligent civilization capable of communications with us. at one star per hour, it would take a single telescope more than 10,000 years to examine that many stars. note that none of this takes into account spread of a civilization capable of interstellar travel. many may not. most that will probably will colonize only a few stellar systems in a 10,000 year civilization lifetime unless faster than light travel can be achieved. making another conjecture, double the number of planets with intelligent life capable of communicating with us. this changes p, V and r by neglible amounts. 3) radio communications consider a radio telescope of area A that can emit a radio beam in a narrow cone of angle alpha radians. if it emits power at the rate of P_e, the power received by a similar telescope, P_r at a distance R is given by P_r = P_e * (A/a), a is area covered by cone at distance R = (P_e * A)/(R^2 * d_sigma), d_sigma is solid angle of cone if we assume that the weakest signal that can be detected is comparable to that of the remnants of the Big Bang, whose spectrum is that of a black body at a temperature of 3 K, an radio telescope of area A will receive a power of E(nu,T) * d_nu * A from space where E is the power per unit frequency per unit area. d_nu is the bandwidth of the telescope, nu is the frequency, and T the absolute temperature. the amount that is actually reflected into the receiver is the part that comes from within the solid angle d_sigma. since only the front half of the telescope is capable of receiving a signal, the fraction of power actually recieved is (d_sigma/2 * pi) for a total power of P_r = E * d_nu * A * d_sigma / (2 * pi) equating the two and solving for R, we get R = 1/d_sigma * ((2 * pi * P_e)/(E * d_nu))^(1/2) the Aricebo radio telescope has a diameter of 300m and a radiating power of about 500,000 W. it's angular resolution is about 10 seconds of arc. if we assume the transmission bandwidth is 1 Hz, a signal transmitted on the 21 cm hydrogen band (10^9 Hz) can be detected to a distance of 3*10^21 m, or about 10^6 ly. for comparison, our galaxy is only about 10^5 ly across. no account is made here of attenuation of the signal by interstellar dust. 4) a communications attempt on saturday, november 6, 1974, a signal was sent from Aricebo toward the globular cluster M-13 in the constellation Hercules, 20,000 ly away. the signal is such that the entire cluster would just be covered by the angle of transmission. M-13 contains about 5*10^5 stars. based upon Sagan's and von Hoerner's estimates of p, there should be between 5 and 0.17 stars with intelligent civilizations in the cluster capable of receiving the signal and perhaps communicating with us. using my more pessimistic estimate, there is less than 1 per cent chance of there being one. the power received, P_r, in M-13 by a telescope comparable to Aricebo would be about 10^-22 W. the power from the background radiation of the Big Bang, P_b, would be about 10^-24 W. the signal to noise ratio is about 20 dB. 5) sending information we can rearrange the expression for R to solve for the bandwidth of a channel required to successfully transmit information to M-13 using the Aricebo radio telescope. d_nu = (2 * pi * P_e) / (R^2 * d_sigma * E) substituting appropriate values, we find that the required signal bandwidth is about 2*10^3 Hz. from information theory, the maximum information transfer rate on a noisy channel is given by R_d = d_nu * log_2(1 + P_r/P_b) = 10^4 bits/s assuming an error correction code of some kind for more reliable communications, this cut to about 3*10^3 bits/s. a typical book contains about 10^6 characters. if we assume that the book is ASCII encoded, this represents about 10^7 bits. a typical book then is transmitted in about 3*10^3 seconds. assuming a billion (10^9) books can contain all the current knowledge of mankind, 3*10^12 seconds are needed to transmit all this information. this is equivalent to about 2.5 million years.
peter@baylor.UUCP (Peter da Silva) (08/29/85)
> >You're assuming there's only a few intelligent races in the galaxy. Besides: > >why would a reace with a low exploratory/reproductive/etc. drive acquire > >interstellar travel? And so what if they can survive for 1000 years on a > >single solar system: that still leaves time for 3,000 iterations of the > >explore/colonise/fill a solar system/explore cycle if they're only 1% > >ahead of us. And do they have to fill the solar system before they want to > >go for the next one? > > you're assuming there are many. No I'm not. I'm just assuming that colinisation is possible. It certainly looks like it is. There are no physical laws that prevent it... they may make it difficult (it may take 1000 years to travel to the next star in a converted asteroid), but it's pretty unlikely to be possible. Let's say that we have a race with the capability to keep a small ecosystem going for 1000 years. I don't see that we won't be able to by the time we get around to chucking asteroids around. Let's say that they're inquisitive and dedicated... like us. They send out half a dozen of these ships. 1000 years later they arrive at the next system and start building a civilisation. Being acclimitised to life in space they're not likely to need planets, just energy and matter: a common resource in the vicinity of stars. I'm sure that within 500 years they're ready to send out another one. Likely the crew will just want to plant a colony and keep on going (who wants to live near a star? They're dangerous! Useful for fuel but dangerous!), but maybe thhey'll want to hang around & have a bunch of kids. Let's assume an average distance between usable stars of 7.5ly. This may be high or low, but it will do for a first approximation and is certainly about the right order of magnitude. OK. Pretty soon you'll have a sphere of these ships expanding at .5% of the speed of light. In a million years that sphere will have filled a pretty nice chunk of the galaxy. In 12 million years it will have filled the whole thing. Probably less, as advances in science speed things up and heavy duty radicals and dissidents head for the REALLY distant parts of the galaxy. -- Peter (Made in Australia) da Silva UUCP: ...!shell!neuro1!{hyd-ptd,baylor,datafac}!peter MCI: PDASILVA; CIS: 70216,1076