Exploration of the Galaxy by self-replicating probes

Our starting point is as in Freitas (Reference Freitas1980b) and Tipler (Reference Tipler1980). This relies on two technologies, which we do not have at present, but which it is reasonable to suppose we will attain within the next few hundred years:

• (T1) A propulsion system capable of sending probes to nearby stars, at say 0.01c.

• (T2) An AI system which, in total, is able, with the resources found in most star systems, of replicating itself.

Propulsion systems. Although no existing system can reach these speeds, various proposals for 100 year probes to Alpha Centauri have been made, such as Project Daedalus. A speed of 0.01c does not seem unduly optimistic, and in fact many proposals for galactic exploration, such as Bjørk (Reference Bjørk2007), consider probes which travel at 0.1c.

AI systems Again, we do not have self-replicating systems at present, and what such a system would be like must rely largely on conjecture. In this context, note the following remark in Wiley (Reference Wiley2012):

A common tendency has been to imagine a self-replicating machine as being rather like a bacterium: that is a single machine which (somehow, almost magically) is able to move around in its environment and replicate itself. If we start with present technology, we are forced to imagine something rather different. The system as a whole might consist of three parts:

1. (A) A number of robots and probes, of several different types, which are together capable of exploring a Solar System and gathering resources (metals, volatiles, etc).

2. (B) A ‘slow assembler’ which would be able to refine these materials into components, which would make the final factory (C).

3. (C) A large-scale factory, or collection of factories, which would be able to manufacture copies of (A) and (B), as well as additional surveying and communication devices.

The payload of the probe would consist of (A + B), together with enough raw materials (fuel, etc.) to get started in the new system. Once (C) was made, resources would be gathered for as long as was necessary, and a number of probes would then be sent to nearby stars. If we take this view, then a ‘SRP’ would not be a single machine, but rather a collection of different machines with an overall capability of replication.

See Freitas (Reference Freitas1980b) for a much more detailed description of such a probe, with the probe (A + B) plus the fuel for the voyage having a mass of of around 10¹⁰ kg. The factory described there only makes one new probe every 500 years, but (see Section 7.1) using a longer period for the initial construction gives a larger factory that can create 1000 new probes in 1500–2000 years. For simplicity I will take the reproduction time, between the arrival of the initial probe in a star system, and the completed factory (C) sending out new probes, to be T _R = 1000.

The AI needed for such a system far exceeds what is possible at present. However, while the kinds of decisions necessary for the AI (e.g. ‘what kind of material is present in this asteroid?’, ‘can it be transported to the factory?’) would require a very high level of skill, this would be within fairly narrow parameters, and a human level of overall initiative and judgement would not be required. Even if machines with a human intelligence can be constructed, it might be desirable to limit the intelligence of the SRPs.

As Tipler (Reference Tipler1980) notes, there are reasons other than stellar exploration to develop these technologies. Progress in AI has been far slower than supposed by early optimists, but it still seems reasonable to suppose that, within a few hundred years, we will be able to build such SRPs. The development of such machines would, at least for a while, introduce an age of plenty, since it would open up the resources of the Solar System for our exploitation. Some idealistic individuals or groups might then be willing to invest the resources in making a number of the probes (A + B), and send them to nearby stars. (See Mathews Reference Mathews2011 for another proposal to explore the galaxy by SRPs.)

Exploration strategy

I now propose a scheme for galactic exploration, assuming that we do develop the technologies (T1) and (T2) described above. The first step would be to send probes to the 10–100 nearest stars, which are all within about 20 ly of Earth. (Long before the start of such a mission we will have very good data on the planetary systems of these stars.) The probes would arrive at their destinations 400–2000 years after the mission start. They would remain in radio contact with Earth (with a time lag of 40 years or less), would report on their discoveries, and would be able to receive updates on strategy. (Among the exploration devices (A) would be systems able to transmit and receive narrow band radio or laser communication over a distance of say 100 ly.)

I will call the initial star systems Level 1 ‘colonies’, though there is no suggestion that they would have a human population. After the construction of the factory (C) on a Level 1 colony, the colony would send out SRPs (let us say about 1000–10 000) to create colonies at ‘Level 2’. I have suggested an initial ‘hop size’ of 10–20 ly, since the number of probes that could be sent out from our Solar System might be limited by resource constraints. However, once a colony at Level 1 or higher had a working factory, there would be no such limit on the number of probes that could be sent out, and it would be sensible to send as many as was necessary to explore every star system within the second ‘maximum hop size’. There are about 15 000 stars within 100 ly of Earth, so with some useful duplication the Level 1 systems would together be able to send probes to every star in this region.

The maximum hop size h _m would be the greatest distance such a probe could be sent with a probability greater than 90% of arriving. I will take h _m = 100; this also needs to be less than the maximum distance for radio or laser communication, but this is much greater than 100 ly.

The probes from the Level 2 colonies would then establish Level 3 colonies and so on. Each colony at Level n would report back to its Level n − 1 ancestor, and receive updating instructions from it. While it would be desirable for the Level 1 colonies to produce many probes, as the radius of the exploration sphere became larger, and so the curvature of its surface became less, fewer new probes per colony would be needed.

Within a few thousand years of the mission start, our descendants on earth (if they still existed) would be receiving a flood of information from the exploration of hundreds of star systems. The Great Pyramid was built around 4500 years ago; 4500 years after its start, the mission would be well under way, and would have given us detailed data on every star system within about 30 ly of Earth.

The overall mission would continue until the planetary system of every star in the galaxy had been explored. Let v _p = 0.01c be the speed of the probes, and v _e be the propagation speed of the exploration front. Then

$$v_{\rm e} = \displaystyle{{h_{\rm m}} \over {T_{\rm R} + h_{\rm m} /v_{\rm p}}} = v_{\rm p} \displaystyle{1 \over {1 + v_{\rm p} T_{\rm R} /h_{\rm m}}}. $$

So T _R = 1000 and h _m = 100 give v _e/v _p = 10/11, the exploration front travels at nearly the same speed as the probes, and the total time to explore the galaxy is around 10⁷ years. This compares with exploration times of the order of 10⁸ years given by Bjørk (Reference Bjørk2007), using probes that travel at 0.1c, but do not replicate.

Implications for SETI and Fermi's question

Let us now make the hypothesis (H) that the technolgies (T1) and (T2) can be attained, and explore the consequences. The exploration scheme outlined above, using these technologies is one which, if it survives long enough, the human race might adopt – no doubt with a number of improvements. The payoff is that with a relatively low initial cost our descendants would obtain detailed data about every star system in the Galaxy. In particular, they would learn how many planets support life, what kind of life it is, and just how rare complex or intelligent life is.

If there have been technological ETI in the Galaxy, then they would also have had this option. So – this is Fermi's question “Where are they?” (This is often called the ‘Fermi paradox’, but it is only a paradox if one begins with the assumption that intelligent life is common. In fact, we have no information on this).

Let us recall the Drake equation, slightly modified for our purposes:

$$N = R^ * \cdot f_{\rm p} \cdot n_{\rm e} \cdot f_{\rm l} \cdot f_{{\rm ci}} \cdot L;$$

here N is the number of existing civilizations sending out SRPs, R* is the rate of star formation per year in the Galaxy, f _p is the fraction of those stars that have planets, n _e is the average number of planets that can potentially support life per star that has planets, f _l is the fraction of these that develop life, f _ci is the fraction of these that develop civilizations that send out SRPs, and L is the average lifetime of such civilizations. This lifetime is the time that either the civilization itself, or its SRPs, remain active. (From now on, I will use the term ‘civilization’ for ‘civilizations that send out SRPs’.)

We do have estimates of at least the order of magnitude of some of the early terms in this expression: for example R*≃7, and data from the Kepler satellite suggests that f _p*≃0.5, while n _e is quite small. (Out of about 10 000 systems surveyed, only a handful have planets which look really promising from the point of finding earthlike life.) At present f _l and f _ci are utterly unknown, though estimates of f _l may at some point become available via spectroscopic search for oxygen.

I have given the Drake equation in a simple form. A more realistic equation would take account of randomness, and the fact that these factors are not constant in time – see for example Glade et al. (Reference Glade, Ballet and Bastien2012). However, the uncertainty in our knowledge of the parameters in the equation is so great that these refinements seem to the author of this article to add little to what can be achieved with a simple ‘back of an envelope’ calculation.

Let us now set

$$\lambda = R^ * \cdot f_{\rm p} \cdot n_{\rm e} \cdot f_{\rm l} \cdot f_{{\rm ci}} = N/L;$$

so that λ is the number of civilizations arising per year in the Galaxy. As an upper bound, if f _l=f _ci = 1 (surely very unlikely) and n _e = 0.03, we obtain λ ⩽ 0.1. Let us set T = 1/λ to be the average length of time in years between successive civilizations arising in the Galaxy; the estimates above suggest it is unlikely that T < 10.

Let us now consider the ‘galactic ecology’ in terms of the two parameters T = λ ⁻¹ and L. Although a better model would allow for randomness of L, a simple mean model already yields useful insights. Figure 1 shows a plot of log L against log T. Since the Galaxy is about 10¹⁰-years-old, we have log L ⩽ 10, and it seems reasonable to take also log L ⩾ 2. The estimates above give log T ⩾ 1. We have no upper bound on T: it is not legitimate to use the Copernican principle to assert that because there is at least one potential civilization in the Galaxy (us) then T ⩽ L. Civilizations might only arise in one Galaxy in a billion, and those that arose would still observe themselves to be in a Galaxy. In the diagram I take 1 ⩽ log T ⩽ 14.

Fig. 1 Galactic ecology parameter space.

Let us now consider the various regions of the diagram. The descriptive statements for the regions apply to typical points in the region – naturally these will become weaker if the point (log T, log L) is close to the boundary between regions.

(R ₁) (‘Alone’) If log T > 10 then probably no other civilization has arisen in the Galaxy. (A more accurate statement would be that the mean number of such civilizations is less than 1.)

(R ₂) (‘Pompeii’) If log T ⩽ 10 and log L < log T then N < 1 and there is no other civilization existing now. However, 10¹⁰/T ⩾ 1 civilizations have existed, and their ruins await discovery – except that we may not last long enough to find them.

(R ₃) (‘Galactic hegemony’) log L ⩾ log T ⩾ 7. We have seen above that in a time of about t _e = 10⁷ years a civilization can explore the Galaxy via SRPs. If this civilization lasts longer than that, and no other civilization arises during the exploration period, then the exploring civilization would attain ‘galactic hegemony’. It would know of the existence of any other civilization that might arise, and would be able to control their growth and activities.

In the remaining parts of the diagram there are many civilizations in the Galaxy. Assume for simplicity that the Galaxy is a uniform disc of thickness h _G = 1000 ly and radius R _G = 50 000 ly, that civilizations arise uniformly in the Galaxy at rate λ, start exploring the Galaxy by SRPs with an exploration speed of v _e = 0.01c, and continue to do so until the civilization (and the SRPs) end L years after the start of the exploration. (A more detailed analysis would take account of the likely existence of a galactic habitable zone described by Lineweaver et al. (Reference Lineweaver, Fenner and Gibson2004).)

If a civilization starts at position x ₀ and time t ₀, then the space-time region explored will be the cone consisting of the points (x, t) such that t ₀ ⩽ t ⩽ t ₀ + L, and | x − x0 | ⩽ v _et. (This neglects for the moment the hard question of interaction between civilizations.) A point (x, t) will be explored by some civilization if any civilization starts in the space-time region

$$C_P (x,t) = \{ (y,t - s):0 \leqslant s \leqslant L,|x - y| \leqslant v_e s\}. $$

The space volume explored will initially grow cubically with L, but with a transition to quadratic growth at the time t _w = h _G/v _e taken to cross the thickness of the galactic disc. We have t _w = 10⁵, and it turns out that it is the case L ⩾ t _w which is of interest. The (space-time) volume of C _P(x, t) is of the order of

$$W_C = \displaystyle{\pi \over 3}h_{\rm G} v_{\rm e}^2 L^3 ;$$

the exact value will depend on its location within the Galaxy. The volume of the Galaxy is V _G = ΠR ²_Gh _G, and so the mean number of civilizations arising in the region C _P(x, t) is

$$M = \displaystyle{{\lambda W_C} \over {V_{\rm G}}} = \lambda \displaystyle{{h_{\rm G} v_e^2 L^3} \over {3h_{\rm G} R_{\rm G}^2}} = \displaystyle{{L^3} \over T}\displaystyle{{v_{\rm e}^2} \over {3R_{\rm G}^2}}. $$

Taking 3R ²_G = 7.5 × 10⁹ ≃ 10¹⁰ ly³, we have M ⩾ 1 when

$$3{\rm log}L \geqslant 14 + {\rm log}T.$$

(Note that log T ⩾ 1 then gives L ⩾ t _w.) If M ≫ 1 then a typical space-time point in the Galaxy will lie in the exploration cone of many civilizations, and so these cones will cover most of the Galaxy, while if M ≪ 1 then there will be substantial vacant unexplored regions.

(R ₄) (‘Multiple zones’) In the region 3 log L ⩾ 14 + log T, log T ⩽ 7 we therefore expect that the galaxy will covered by the zones of control of more than civilization. How these civilizations might interact is considered briefly below.

If 3 log L ⩽ 14 + log T then civilizations are too rare and short-lived for their SRPs to cover the Galaxy, but we can still ask about their radio signals. Let us begin by considering the conditions for 2-way communication by radio with an ETI. The same analysis as with the SRPs applies in this case, but with v _e replaced by the speed of light v _c = 1. Assume for simplicity that the time between a civilization starting to send out radio transmissions and sending out SRPs is small, and that radio transmissions continue for the lifetime of a civilization. Then the mean number of civilization still extant whose broadcasts can be accessed at a point (t, x) will be

$$M' = \displaystyle{{L^3} \over T}\displaystyle{{v_c^2} \over {3R_{\rm G}^2}} = \displaystyle{M \over {v_{\rm e}^2}}. $$

Thus, M′ ⩾ 1 if 3 log L ⩾ 10 + log T. (If log T ⩾ 1 then this condition gives L ⩾ 10^11/13 > 1000, so the case when we need to consider zones with radius less than h _G does not arise.)

(R ₅) (‘2-way SETI’) If 10 + log T ⩽ 3 log L ⩽ 14 + log T and log T ⩾ 1 then a typical point will be able to receive radio signals from a civilization which is still extant, but will not be visited by SRPs. There is therefore the possibility of 2-way communication by radio between two civilizations, possibly continuing until one becomes extinct. This is the situation envisaged in much of the early SETI literature.

(R ₆) (‘1-way SETI’). If 3 log L ⩽ 10 + log T and log T ⩾ 1 then a typical point can only receive signals from extinct civilizations. A point (t, x) will be able to receive signals from a civilization if that civilization arose in the region

$$C_S (t,x) = \{ (y,s):t - |x - y| - L \le st - |x - y|\}. $$

This has space-time volume LV _G, and so the mean number of such civilizations is λLV _G/V _G = L/T. Thus, L ⩾ T is (not surprisingly) also the condition for there to be some civilization in the Galaxy within our light cone.

The space of galactic ecologies is therefore divided into six regions. For regions R ₁ and R ₂ there is little more to be said, but some other cases deserve further attention.

In region R ₄ a typical point in the Galaxy could be explored by SRPs from many civilizations, and it is necessary to consider how such civilizations might interact. One can identify three broad possibilities:

1. (i) No interaction, and mutual interpenetration between explored regions of different civilizations;

2. (ii) Civilizations establish boundaries between their different ‘zones of control’;

3. (iii) Civilizations (or their SRPs) engage in warfare.

In case (i) we would expect to see many probes within our Solar System, and our failure to do so tends towards excluding this possibility.

For case (ii), consider the arrival of an SRP from Civilization X in a star system already containing infrastructure built by Civilization Y. The probe would need to decelerate from 0.01c, and this would require the expenditure of large amounts of energy over a significant period, making the arrival detectable by Y. On arrival the SRP would have limited fuel and resources, and could be quarantined or neutralized by Y. A (lengthy) period of negotiation might then lead to agreed boundaries between X and Y.

If negotiation failed then war might ensue, which is case (iii). In the case of all out war, constraints on the number of SRPs built would be dropped, and all available material would be used. If it is the case that the material in stars and gas giants is too tightly bound gravitationally to be used to make SRPs, then the effects of such a war on other star systems might not be detectable to us at present. However, two pieces of evidence support the conclusion that such a war has never occurred in our Galaxy. The first is that the Solar System has not been mined in this way. Second, if SRPs can only utilize smaller planets then the total mass usable for SRPs in a typical stellar system would be around 10²²–10²³ kg. However, a protostellar nebula contains a mass of around 10³⁰ kg, which is not so tightly bound gravitationally. Such nebulae would be major military prizes, and their continued existence in our Galaxy, as well as that of recently formed stars, suggests that our Galaxy has seen neither an all out war, nor an arms race. (This applies also to other galaxies.)