Table Of ContentPreface
This textbook attempts to tackle the many academic concepts and theories that
guide our thinking about the search for extraterrestrial intelligence (SETI), using
Fermi’sParadoxasalens.Whilewritingit,Ihaveaimedattwoobjectives:
1. Provide an exhaustive list of solutions to Fermi’s Paradox as of the time of
publication,and
2. Provide context to this list of solutions, by describing and explaining their
theoretical/numerical/observationalunderpinnings.
This is no mean feat, and the lack of graduate-level textbooks which attempt to
achieve both objectives is probably an indication. We will see that the question
raised by Fermi’s Paradox requires an extremely broad swathe of academic disci-
plines to formulate a complete set of solutions. In fact, it could be argued that all
academic disciplines have contributions to make, and that SETI is a study of the
humancondition,generalisedtoincludeallsentientbeings.
Obviously, a textbook that requires contributions from the entirety of academe
will be necessarily abbreviated, and in the interests of focus I have been forced to
editoutorignoreaspectsthatwouldotherwisemeritmoreattention.Assuch,this
book should be seen as an introduction to the most pertinent facts and concepts.
Forexample,intheIntroductionIgiveabriefaccountoftheobservationalaspects
ofSETI,butthefieldisworthyoffarmorediscussion.Thiscanbefoundinarange
of excellent textbooks on observational SETI and radio astronomy in general (see
References).
Thisbookisdominatedbyastronomyinitsmake-up,principallybecauseSETI
remainsanastronomy-dominateddiscipline.Whatshouldhopefullybeclearupon
readingthistextbookisthatSETI’saccountingofotherdisciplinesisquiteuneven,
and there are many topics highly deserving of further study. I will do my best to
highlight areas where I believe that further work is necessary, to encourage the
readertohelpfillinthesegaps,sothatsubsequenteditionsofthisbookcandisplay
ourmoredevelopedunderstandingoflifeandintelligenceintheUniverse.
xvii
1
Introducing the Paradox
1.1 FermiandHisParadox
1.1.1 TheParadox,inBrief
Consider the Milky Way galaxy. It is a barred spiral galaxy, corresponding to the
HubbleclassSbc,indicatingitsspiralsarerelativelylooselywound.Itcanbesep-
aratedintoseveralcomponents(bymass):overlappingthickandthindiscsofstars,
gas and dust with spiral structure, an inner bulge (and bar), a spheroidal halo of
relatively old stars and a far greater dark matter halo, which is the most massive
component and encompasses the entire galaxy, extending far beyond its visible
component.
The Milky Way’s stellar disc is approximately 160,000 light-years (about 50
kiloparsecs or kpc) in diameter (Xu et al., 2015). If we consider an intelligent
civilisationthatwishestoexploretheentiregalaxy,itisestimatedthatitcoulddo
soinatimescale,τ atmostonehundredmillionyears,andmostlikelymuch
explore
lessthanthat(wewillexploretherationalebehindtheseestimateslater).
Now consider the Earth. Its parent star, the Sun, orbits the Galactic Centre at
a distance of around 26,000 light-years (around 8 kpc). The Earth’s age is estab-
lished to be at least 4.4 Gyr from radiometric dating of zircons – age estimates of
4.54+0.1 Gyr is determined from radiometric dating of meteorites (see, e.g., Dal-
−0.03
rymple, 2001). Fermi’s Paradox then becomes clear if we express the Earth’s age
inunitsofτ :
explore
τ⊕ > 45τexplore. (1.1)
The Paradox is best described in the language of a logical argument. Formally,
logicalargumentsconsistof:
● asetofpremises(sometimespremisses),statementsorpropositionsassumedto
betrueatthebeginningoftheargument;
3
4 IntroducingtheParadox
● a set of inferences from those premises, derived using (for example) rules of
propositionallogic,and
● aconclusion,astatementorpropositionderivedfromthepremisesandinferen-
tialstepsabove.
A valid argument guarantees the conclusion is true if the premises are true. An
argumentissound ifitisvalidandthepremisesareindeedtrue.Wecantherefore
beinasituationwhereanargumentisvalidbutunsound–thelogicalargumentis
internallyconsistentbutbuiltonpremisesthataredemonstrablyfalse.
Nowconsiderthefollowingpremises:
Premise1. HumansarenottheonlyintelligentspeciesintheMilkyWay.
Premise2. TheEarthisnottheoldestterrestrialplanetintheMilkyWay.
Premise3. Otherintelligentcivilisationsarecapableofmakingthemselvesknown
tous.
Someinferentialstepsmightbe:
Therefore. OthercivilisationscurrentlyexistintheMilkyWay,andhavedoneso
forlongerthanhumanity.
Therefore. Other civilisations have had more than enough time to make them-
selvesknowntous.
Withafinalconclusion:
Therefore. HumansmusthaveevidenceforothercivilisationsintheMilkyWay.
The‘Paradox’isthefactthattheconclusionisfalse–humansdonothaveevidence
for other intelligent civilisations, despite the validity (and apparent soundness) of
theaboveargument.Aswillbecleartothosefamiliarwithformallogic,thisargu-
ment does not in fact constitute a paradox, as we will discuss below. It is a valid
argumentthatarrivesataconclusionthatiscontradictedbyastronomicalobserva-
tions and other scientific evidence. We can resolve this by either showing one or
moreofthepremisestobefalse,makingtheargumentunsound,orshowingoneof
theinferentialstepstoeitherbefalseornotproceedlogicallyfromthepremises.
1.1.2 Fermi’sParadoxIsNotHis,andItIsn’taParadox
ThereisanuglytruthtoFermi’sParadox–atitsbase,itdoesnotbelongtoFermi,
andaswehaveseenfromtheprevioussection,itisnotformallyaparadox.
ItmightbebetterdescribedastheFermiQuestion,theFermi-HartParadox,the
Hart-Tipler Argument or even, as suggested by Webb (2002), the ‘Tsiolkovsky-
Fermi-Viewing-Hart Paradox’, giving Tsiolkovsky the original credit for the
1.1 FermiandHisParadox 5
conceptintheearly1930s.However,themoniker‘Fermi’sParadox’hastakenhold
intheliteratureandtheSearchforExtraterrestrialIntelligence(SETI)community,
sowewillpersistwiththenamethatissomethingofamisnomer.
The origins of what is now called Fermi’s Paradox are typically traced back
to a now-legendary lunchtime conversation at Los Alamos National Laboratory
in 1950, between Enrico Fermi, Emil Konopinski, Edward Teller and Herbert
York, all four of whom were deeply involved in the development of nuclear
technology.
Fermi’sownmemoriesoftheconversationarenotamatterofrecord(Fermidied
in1954).Laterconversationswiththeotherparticipantsareouronlysource(Jones,
1985; Gray, 2015). The timing of the conversation is confirmed by testimony that
indicatesitprecededthe‘Georgeshot’of8–9May1951,anuclearbombtestthat
proved to be a crucial milestone in the development of thermonuclear weapons.
Konopinskirecalledjoiningtheothersastheywalkedtolunch:
WhenIjoinedthepartyIfoundbeingdiscussedevidenceaboutflyingsaucers.Thatimme-
diatelybroughttomymindacartoonIhadrecentlyseenintheNewYorker,explainingwhy
publictrashcansweredisappearingfromthestreetsofNewYorkCity.Thecartoonshowed
whatwasevidentlyaflyingsaucersittinginthebackgroundand,streamingtowardit,‘little
greenmen’(endowedwithantennas)carryingtrashcans.Thereensuedadiscussionasto
whetherthesaucerscouldsomehowexceedthespeedoflight.
(Gray,2015,p.196)
The cartoon also helps us to pin down the date further, to the summer of 1950.
We can already see here the beginnings of the logical arguments that form the
foundationsofFermi’sParadox.FermiisthensaidtohaveaskedTeller:
Edward,whatdoyouthink?Howprobableisitthatwithinthenexttenyearsweshallhave
materialevidenceofobjectstravellingfasterthanlight?
(Jones,1985,p.2)
Teller’sestimateoftheprobabilitywaspessimistic(10−6,i.e.,oneinamillion).
Fermiascribeda10%probability,andthisbecameatopicofdebateuntilthegroup
satdownatlunch(accountsdifferonthetotalnumberofpeoplepresent).Thecon-
versationmovedontoothertopics.Accountsreachconsensusonthenextmoment,
whereFermipronounced,aproposofnothing:
Whereiseverybody?
(Jones,1985,p.3)
The precise wording of the question is also in doubt, but all agree on its sub-
stance.Wherethediscussionpivotedtofollowingthisremarkisalsounclear.Teller
dismissedthesignificanceofwhatwasnextsaid:
6 IntroducingtheParadox
I do not believe that much came from this conversation, except perhaps a statement that
thedistancestothenextlocationoflivingbeingsmaybeverygreatandthat,indeed,asfar
as our galaxy is concerned, we are living somewhere in the sticks, far removed from the
metropolitanareaofthegalacticcenter.
(Jones,1985,p.3)
York suggested that Fermi went on to estimate (in his now famous style) the
probability of Earthlike planets, the probability of life appearing on these planets,
theprobabilityofintelligentcreaturesandsoon.Thesefactorsaredirectancestors
ofthetermsinDrake’sequation,aswewillseeshortly.York’sownadmissionthat
hismemoryofthismomentwas‘hazy’mayleadonetotheconclusionthatYork’s
memoriesof1950areconfabulatedwithsubsequenteventsinthe1960s,whichis
whollyplausible.
SowheredoHartandTiplerfitintothisstory?MichaelHartiswidelycredited
withformulatingFermi’sParadoxasitisunderstoodtoday,andyetdoesnotreceive
theappropriatecredit.InhispaperExplanationfortheAbsenceofExtraterrestrials
onEarth,Hart(1975)declares‘FactA’–thelackofevidenceforintelligentbeings
other than humans on Earth. His argument is simple – if intelligent beings exist,
and they are capable of space travel, then the Milky Way can be colonised on a
timescaleshortrelativetotheEarth’sage,andhenceitseemsthatintelligentbeings
shouldalreadybehere,butarenotaccordingtoFactA.Hartbeginslistingseveral
possible solutions to this incongruity, and is one of the first to publish work on
whatwenowrefertoasFermi’sParadox.
Tipler is usually credited alongside Hart for formulating perhaps the most
binding form of the Paradox. He invokes the universal constructor or von Neu-
mannmachineastheperfectdeviceforgalacticexploration.Essentiallycomputers
capableofprogrammedself-replication,asingleprobecangrowexponentiallyinto
a fleet of probes to rapidly explore the entire Milky Way (we will delve into the
detailsinsection20.1).
Tipler argues that any intelligent species that is capable of interstellar com-
munication will eventually construct von Neumann devices, and as such if other
intelligent beings exist, it is highly likely that the Milky Way has already been
explored. Tipler then invokes Hart’s Fact A to insist that there are no extrater-
restrial intelligences, and consequently the SETI endeavour is fruitless (see, e.g.,
Tipler,1993).
This formulation is largely considered to be the most stringent form of Fermi’s
Paradox, as it is independent of civilisation lifetime. Once an initial probe is
launched, the exploration continues even after a civilisation dies. It also consid-
erstechnologicaltrajectoriesthathumansarepursuing,throughgreaterautomation
and self-sufficiency of computational processes. It seems clear, then, that Fermi’s
Paradoxisstrong,andanysolutiontoitmustalsobestrong.
1.2 DrakeandHisEquation 7
But it is not a Paradox, at least as it is defined by formal logic. In this case,
a Paradox is a set of propositions that results in an ambivalent or contradictory
conclusion (i.e., the final statement can be either true or false, or both). A classic
exampleofaparadoxistheLiar’sParadox,summarisedinasinglesentence:
Thissentenceisalie.
Iftheabovesentenceistrue,thenitisalsoalie.Ifitisalie,thenitisalsotrue.
Fermi’s Paradox doesn’t satisfy this definition of a paradox, or any of its other,
more colloquial definitions (such as ‘a concept containing mutually exclusive or
contradictory aspects’). At best, it describes a logical argument that is valid but
unsound.Thephrase‘Fermi’sParadox’appearstohavebeencoinedbyStephenson
(1977). The celebrity status of Fermi, plus the dramatic allure of the word ‘Para-
dox’,hassuccessfullyimplanteditselfintotheimaginationofbothacademicsand
the general public, even if it is not a strictly correct description of the concept.
For convenience, we will continue to describe the problem at hand as ‘Fermi’s
Paradox’.
1.2 DrakeandHisEquation
In1958,FrankDrake,arecentPhDgraduatefromHarvard,acceptedaroleasstaff
scientist at the National Radio Astronomy Observatory (NRAO) at Green Bank,
West Virginia. Radio astronomy was in its infancy in the United States – Drake
was only the third person to have held his role at Green Bank, which itself was
only founded two years previously. During his graduate studies, Drake had calcu-
lated that military radar with a power of 1 megawatt could communicate with a
counterpartsystematadistanceofapproximately10light-years.
Drake convinced the interim director of NRAO, Lloyd Berkner, to use Green
Bank’s26mradiodishtosearchforartificiallyproducedsignalsonthecondition
thatitwasdonequietly,andthattheobservationswouldyielddatausefulforcon-
ventionalastronomy.BeginningwhathewouldcallProjectOzma,Draketargeted
twostars,TauCetiandEpsilonEridani,forartificialtransmissions.
His preparations coincided with the publication of Cocconi and Morrison’s
(1959)seminalpaperSearchingforInterstellarCommunications.Hisobservations
in 1960 yielded no signs of extraterrestrial intelligence, but his publication of the
attemptbegantonucleateavarietyofthinkersontheconceptofintelligentlife.An
informalmeetingwasconvenedatGreenBankin1961todiscussthepossibilityof
detectingintelligentlife.
In an attempt to focus the discussion, Drake would write his now famous
equationontheboard:
N = R∗fpne fi fl fcL (1.2)
8 IntroducingtheParadox
Thenumberofcivilisationsemittingsignalsatanytime, N,isrelatedto:
R∗ – Therateofstarformation,instarsperyear
f – Thefractionofthosestarswhichhaveplanetarysystems
p
n – Theaveragenumberofhabitableplanetsperplanetarysystem
e
f – Thefractionofhabitableplanetsthatareinhabited
l
f – The fraction of inhabited planets that possess intelligent technological
i
civilisations
f – The fraction of intelligent technological civilisations that choose to emit
c
detectablesignals
L – Theaveragelifetimeofacivilisation’ssignal
Each of these seven parameters has assumed a range of values over the years,
depending on contemporary knowledge of star and planet formation, as well as
rather subjective opinions regarding the evolution of life, intelligence and the
longevity of civilisations. Optimists will typically enter relatively large values for
the initial parameters, resulting in N ≈ L, i.e., that the number of signals extant
is only sensitive to their longevity. A more restrictive argument can easily yield
N < 10−10,indicatingthatwearelikelytobealoneintheGalaxy.
Becauseofthecurrentuncertaintiesinestimatingitsparameters,itisworthnot-
ingthatDrake,andindeednoSETIscientist,regardsDrake’sequationasauseful
toolinactuallycalculatingthenumberofintelligentcivilisationsweshouldexpect
todetect,foravarietyofreasons.
There are two principal issues with the equation, which are its fixed nature in
space and time. It implicitly assumes a steady state of civilisation birth and death
persistsacrosstheentireMilkyWay.Byextension,itassumesthattheastrophysical
constraints on civilisation birth and death have also reached a steady state at all
locationsofinterest.
It is immediately clear to anyone with a grounding in astronomy that with the
exceptionofsomephysicalconstants,theUniversecannotbedescribedasconstant
ineitherspaceortime.TheconstituentsoftheUniverseareperpetuallychanging,
and this is clear at the level of the Milky Way. The propensity of the Milky Way
toproducehabitableplanetshascertainlychangedagreatdealsincetheGalaxy’s
initialdiskstructurewasformedaround9billionyearsago(Haywoodetal.,2016),
andtherearelikelytoberegionsmorehospitabletolife(andintelligentlife)than
others (see section 4.2.2). It is possible to allow the seven factors to evolve with
time,producinganumberofcommunicatingcivilisationsthatalsovarieswithtime,
N(t),butconstructingfunctionstodescribethetimedependenceofeachparameter
is challenging. Many authors have discussed how folding in our understanding of
starformationhistoryintheMilkyWay(i.e.,theformof R∗(t)),andtheproperties
1.2 DrakeandHisEquation 9
of the initial mass function (broadly, the probability distribution of stellar mass)
canmake N varygreatlywithtime.
It is also clear that the availability of chemical elements with atomic numbers
larger than helium (what astronomers call metallicity) changes greatly with time,
asseveralgenerationsofstarformationcreateheavierelementsvianuclearfusion,
which are then expelled in stellar death. Sufficiently rich chemistry is a prerequi-
siteforprebioticmolecules(andsubsequentlylife),soafunctionthatdescribes f
l
will contain a term that grows in tandem with growing metallicity. These evolu-
tionarytrendshaveledmanytoproposethatFermi’sParadoxresultsfromaquirk
oftiming,aswewillseeinsection18.2.
Even if suitable functions are found for each variable, Drake’s equation still
struggles to inform us where to look for technological civilisations. Manipulating
Drake’sequationmaynotyieldamoreusefulexpression,butitcandeliverinsight.
Maccone (2012) notes that we could consider an extended form of the equation,
wherethesevenfactorsarere-expressedasalarge(effectivelyinfinite)numberof
sub-factors X .Theequationwouldnowconsistofthefollowingproduct:
i
N = (cid:3) X (1.3)
i i
Let us now assume each factor X is instead a random variable. If we take the
i
logarithmofthisequation:
(cid:2)
logN = logX (1.4)
i
i
then we are afforded insight to the properties of N via the Central Limit The-
orem. Consider a set of independent random variables [X ], which may have
i
arbitraryprobabilitydistributionswithmeanμ andvarianceσ2.TheCentralLimit
i i
Theorem guarantees that the sampling mean of these random variables is itself
a random variable with a Gaussian distribution (provided that the variances are
finite).ThisimpliesthatlogN isnormallydistributed,orequivalently N islognor-
mally distributed. What is more, the parameters that define the distribution of N
aredeterminedbytheparametersthatdefine X :
i
(cid:2)
1
μ = μ (1.5)
N N Xi
i
(cid:2)
1
σ2 = σ2 (1.6)
N N Xi
i
Andthemeannumberofcivilisationsishence
N¯ = eμNeσN2/2 (1.7)
