Annihilating aliens & Rare Earth suggest early filter

epistemic sta­tus: I sus­pect these thoughts are not novel and are po­ten­tially wrong. I still think there’s some value in record­ing my thought process

tl;dr: Selec­tion effects from not be­ing an­nihilated by aliens may ex­plain why we don’t see any very ad­vanced aliens, but it doesn’t ex­plain why don’t see any as ad­vanced as we are. This may sug­gest a filter be­hind us.

Civil­i­sa­tions may some­times be­come suffi­ciently ad­vanced to spread across the stars. Per­haps they would even ex­pand out­wards in a near light-speed “shock­wave” that con­verts all available re­sources into some­thing that they value (like copies of their mind). Per­haps they send seed ships across in­ter­galac­tic voids. Wher­ever they go, no new civil­i­sa­tions arise: all mat­ter and en­ergy is used by their civil­i­sa­tion.

Sup­pose we live in a uni­verse of in­finite spa­tial ex­tent, and that there’s some chance of in­ter­galac­tic civil­i­sa­tion aris­ing in any un­oc­cu­pied spa­tiotem­po­ral re­gion. If these civil­i­sa­tions spread out at near light-speed and the chance of civil­i­sa­tional gen­e­sis is less than a cer­tainty, there will always be an in­finite ex­tent of un­colon­ised space through­out the his­tory of this uni­verse. The pic­ture be­low shows an ex­am­ple of such a re­gion in a world where civil­i­sa­tions arise rel­a­tively of­ten.

A busy world with space left

After a lit­tle thought, it might ap­pear that we have an an­thropic solu­tion to the Fermi Para­dox here: of course we don’t ob­serve any aliens, for if if we were in their fu­ture light cone, the mat­ter we are made of would be used for some­thing else, so we wouldn’t ex­ist.

Be­fore we rush ahead with this line of think­ing, let’s look at a cou­ple of caveats with this idea. The first is that civil­i­sa­tions may ex­ist in states that are ob­serv­able but not sub­sum­ing. I’ll speci­fi­cally con­sider the case where civil­i­sa­tions start of as ob­serv­able for a pe­riod, then be­come sub­sum­ing. The sec­ond is the ob­served age of the Uni­verse and its im­pli­ca­tions for this ar­gu­ment.

Visi­ble but not subsuming

On the first, our civil­i­sa­tion has prob­a­bly been ob­serv­able for awhile, given the amount and struc­ture of elec­tro­mag­netic ra­di­a­tion we pro­duce. If we pre­sume that this “young” pe­riod is typ­i­cal for civil­i­sa­tions, we have to ex­plain why we don’t ob­serve any young civil­i­sa­tions that wouldn’t have sub­sumed us yet.

Let’s take a model where a young civil­i­sa­tion de­ter­minis­ti­cally be­comes an in­ter­galac­tic civil­i­sa­tion over some pe­riod τ. Then we have to won­der why there are no young civil­i­sa­tions in the red love­heart re­gion of the pic­ture be­low.

Immature civilisations in the red region are observed but do not annihilate us

The vol­ume of a past light cone at time t scales like t⁴, and if p is the prob­a­bil­ity that a civil­i­sa­tion arises in a vol­ume of space­time, the prob­a­bil­ity that a light cone con­tains no civil­i­sa­tions scales like (1 - p)^(t⁴). This of course drops off very fast with in­creas­ing t.

The prob­a­bil­ity, B, that there are no civil­i­sa­tions aris­ing in the red re­gion looks like (1 - p)^(t⁴ - (t - τ)⁴).

Per­haps we think we are rel­a­tively close to be­com­ing in­ter­galac­tic (even up to a mil­lion years away would count for my pur­poses). That sug­gests that τ is very much smaller than the pe­riod of the Uni­verse’s his­tory in which life might have arisen. There­fore, we might kill off terms in the ex­po­nent of B that are in higher pow­ers of τ. This gives us a prob­a­bil­ity that scales like (1 - p)^(τ⋅t³). This still scales very fast with t, so p still can’t be very great, but given low τ, higher val­ues of p be­come plau­si­ble.

Young in an old world

Now to the age of the Uni­verse. For a young civil­i­sa­tion to come into ex­is­tence in some re­gion, it has to be the case that no ma­ture civil­i­sa­tions ex­ist in that re­gion’s past light cone and that the ap­pro­pri­ate con­di­tions are met for civil­i­sa­tion to arise.

The chance that a spa­tiotem­po­ral re­gion’s past light cone doesn’t in­clude ma­ture civil­i­sa­tions de­clines with that re­gion’s po­si­tion in time (very quickly, as seen above): later re­gions have larger past light cones that we re­quire no civil­i­sa­tions to have ex­isted within. If we as­sume that the chance of a civil­i­sa­tion aris­ing in a re­gion does not in­crease through­out time, the prob­a­bil­ity a young civil­i­sa­tion ob­serves a young uni­verse is far greater than that it ob­serves an old uni­verse. Our in­finite uni­verse ar­gu­ment says that there are young-old civil­i­sa­tion-uni­verse com­bi­na­tions, but that young-young is more prob­a­ble.

Given that it seems plau­si­ble that the Uni­verse could have sus­tained life for a long time be­fore we came around, this pushes us back to­wards some­thing like a Fermi para­dox. Not: “where is ev­ery­one?”, but: “(why) are we late to the party?”

A filter behind

This can be re­solved with a Rare Earth hy­poth­e­sis, just like the nor­mal Fermi para­dox. That is, we could say it’s very difficult to be­come an in­ter­galac­tic civil­i­sa­tion. Even though that doesn’t change the fact that early in­ter­galac­tic civil­i­sa­tions are more prob­a­ble, if it re­ally is as­tound­ingly difficult to be­come in­ter­galac­tic, the prob­a­bil­ity of ob­serv­ing an old(ish) Uni­verse is not ap­pre­cia­bly less than ob­serv­ing a young one.

One might even be tempted (in­suffi­ciently, ac­cord­ing to me) to say that young civil­i­sa­tions are very com­mon, but that all of them die out. That way, you don’t need to worry about ex­pan­sion-shock­waves in your past light cone. In fact, pretty much the same pro­por­tion of space will be available for new civil­i­sa­tions for all time.

I don’t think the last para­graph holds. Con­sider again the pic­ture with the blue teardrop and red love­heart re­gions. What­ever the nor­mal life­time of a young civil­i­sa­tion (even if it in­evitably never be­comes old), there is some red re­gion where young civil­i­sa­tions would be ob­served.

Let’s model be­com­ing an in­ter­galac­tic civil­i­sa­tion as a two step pro­cess. Be­com­ing a young civil­i­sa­tion with prob­a­bil­ity y and (af­ter time τ), go­ing from young to in­ter­galac­tic with prob­a­bil­ity i. The prob­a­bil­ity of an in­ter­galac­tic civil­i­sa­tion aris­ing in an ap­pro­pri­ate re­gion then is c = yi.

The age of the Uni­verse sug­gests c is low. So at least one of y and i must be low. If i were very low and y high, then we might ex­pect a teem­ing red re­gion—we would ob­serve a lot of young civil­i­sa­tions. So that sug­gests that (at least) y is low and that there is a Great Filter is be­hind us.

An­thropic principles

The ar­gu­ment above is es­sen­tially us­ing the self-sam­pling as­sump­tion. We con­sider a world with var­i­ous young civil­i­sa­tions, and imag­ine we are drawn from the set of these young civil­i­sa­tions. What is the prob­a­bil­ity that we see empty skies? What is the prob­a­bil­ity that we see the Uni­verse is old?

How does the above ar­gu­ment need to be changed un­der the self-in­di­ca­tion as­sump­tion? I’m not that con­fi­dent in this bit, but here’s my think­ing: if the pos­si­ble wor­lds we se­lect from are ob­tained by vary­ing the pa­ram­e­ters i and y in the above model, we ex­pect y to be high (as Katja Grace has pointed out) be­cause that re­sults in more ob­servers that we could be cho­sen from. The only other way to in­crease the prob­a­bil­ity of empty skies (in this model) is to shrink down τ, thus re­duc­ing the vol­ume of the red re­gion and sug­gest­ing that the time from trans­mit­ting sig­nals to judg­ment day is short.