Estimating remaining lifetime of humanity

Transcription

1 Estimting remining lifetime of humnity Yigl Gurevich Astrct In this pper, we estimte the remining time for humn existence, pplying the Doomsdy rgument nd the Strong Self-Smpling Assumption to the reference clss consisting of ll memers of the Homo spiens, formulting clcultions in trditionl demogrphic terms of popultion nd time, using the theory of prmeter estimtion nd ville pleodemogrphic dt. The remining lifetime estimte is found to e 70 yers, nd the proility of extinction in the coming yer is estimted s 0.43%.. Introduction Modern humns, Homo spiens, exist ccording to ville dt for t lest 30,000 yers [4], [5]. It is interesting, however, to estimte the time remining for the survivl of humnity. To determine this vlue there ws proposed the so-clled doomsdy rgument [] - proilistic resoning tht predicts the future of the humn species, given only n estimte of the totl numer of humns orn so fr. This method ws first proposed y Brndon Crter in 983 []. Nick Bostrom modified the method y formulting the Strong Self-Smpling Assumption (SSSA): ech oserver-moment should reson s if it were rndomly selected from the clss of ll oserver-moments in its reference clss. [3]. In this pper, we pply the SSSA method to the reference clss consisting of ll memers of our species, formulting clcultions in trditionl demogrphic terms of popultion nd time, using the prmeter estimtion theory nd the ville pleodemogrphic dt.

2 To estimte the remining time t we will fulfill the ssumption tht the oserver hs n equl chnce to e nyone t ny time. Of course the ssumption is philosophicl nd somewht metphysicl. Religious people would hve formulted it s "the soul hs n equl chnce to e in this or tht ody." However, t lest this ssumption is simple, symmetricl nd devoid of ny self-centeredness. The demogrphic history of mnkind cn e shown on grph (Fig. ), tht hs the time x on the horizontl xis nd the popultion y = h (x) on the verticl xis. The initil moment of history denoted, nd the end, tht is the time of the disppernce or deth of humnity, denoted. The present moment, tht is the moment of oservtion, denoted x 0 - sometimes, however, we will simply denote it x. Exmple of popultion history y = h (x) x0 Fig.. Let f(x) = p (x 0 = x h), where p - the conditionl proility density of oservtion moment for given function h. Let F(x) the relted distriution function:

3 F(x) = f(τ) dτ, H(x) is the integrl function of pssed person-yers x x H(x) = h(τ) dτ nd S is the totl numer of person-yers during the existence of mnkind S = H(). From our ssumption, we get: f(x) = h(x) / S () nd F(x) = H(x) / S. (). The proposed estimtor The left side of the grph, tht is, vlues h(x) on the intervl [,х 0 ], is n oservtion dependent on S. It is proposed the following estimte of the prmeter S: S = H(x), (3) where х - the time of the oservtion. Sttement. Estimtor S (3) is unised estimtor of the prmeter S. Proof. For ech S > 0 E[S ] = E[H(x)]. Considering (), E[S ] = f(x)h(x)dx = S H(x)h(x)dx. By chnging the vrile of integrtion u=h(x), we get E[S ] = S u du = u S S 0 = S. S Lemm. 0 3

4 P(S < ks) = k, for ech k [0,]. (4) Proof. Considering (), P[S < ks] = P[ H(x) < ks ] = P[ F(x)S < ks ] = P[F(x) < k ] = k, (3) for n ovious property of the distriution function. Sttement. S is n medin-unised estimtor of the prmeter of S. Proof. This follows from Lemm t k =. We compute the men solute devition d of estimte S : d = S S f(x) dx = H(x) S f(x) dx = S F(x) f(x) dx. Sustituting u=f(x), we get: d = S u du 0 = S [ u / 0 + u / 0 + u / = S [ (u ) du 0 u / + (u ) du ] = S ( + ) = S. 4 4 We clculte the vrince D nd the stndrd devition σ of estimte S : D = (S S) f(x) dx = S (F(x) ) f(x)dx. Sustituting u=f(x), we get: 0 = (H(x) S) 0 D = S (u ) du = S [ 4u du f(x)dx = 4udu + ] = du ] = 0 0 = S [ 4 3 u3 0 u 0 + u 0 ] = S ( ) = S 3, σ = S 3. Now, on the sis of the estimte of S we cn estimte the vlue of x R = h(t)dt = S H(x) (5) 4

5 s R = S H(x) = H(x) H(x) = H(x). (6) 3. Applying to the historic dt Let pply (6) to our prticulr historicl sitution where x = 05 (yer). Historicl popultion dt is tken from [4]. According to [5] t the time tht the species Homo Spiens originted, etween 30,000 nd 90,000 yers go, its popultion ws etween 0,000 to 35,000 people. We will tke the middle points of these rnges: = , h () = 500. Popultion dt etween nd 000 is tken from [4], [6], nd fter the yer 000 from [4], [7]. The used dt re shown in Tle nd Fig World popultion history y = h(x) Fig.. x h, Mil x h, Mil

6 Tle. Using these dt s points for the trpezoidl rule, we otin H(05).7 0 (person-yers), nd consequently, ccording to (6) the sme estimte for the remining numer of person-yers: R =.7 0. (7) We now turn to estimte the remining time of humn existence, tht is the vlue t = x 0, where x 0 = 05. We use prediction from [8] (see. Fig. 3): 6

7 Fig. 3 As you cn see, the verge prediction for 00 exceeds illion, ut the growth is slowing down, nd then you cn expect stiliztion or even decrese in the numer. Therefore, we tke s chrcteristic numer for the period x > 05 vlue ĥ = 0 0 (8) nd using (7) we otin n estimte of the remining time t s t = R =.7 0 = 70 (9) ĥ 0 0 nd n estimte of the lst yer of humn existence is = x 0 + t = = 85. But it is, of course, only medium estimte. Designting L = H(x 0 ) и considering (3), (5) и (6), we get from (4): k = P[S < ks] = P[L < k(l + R)] = P[L < kl + kr] = = P [ (-k)l < kr ] = P[ R > k ]. L k Sustituting q = k, k = we otin k q+ for q >= 0. P ( R L > q) = q + 7

8 Assuming h is constnt for x > x 0 we get P ( tĥ > q) =. L q+ Sustituting z = Lq/ĥ, we get P(t > z) = = zĥ L + z (0) t + The following chrt shows the proility of mnkind to survive certin numer of yers for the vlue t from (9). Proility to survive Fig. 4 We now clculte more ccurtely the proility to exist one next yer. Let ĥ = , ccording to the dt for 06 yer from [7]. Then L =.7 0 = 30, ĥ nd from (0) we get P(t > ) = = nd the opposite proility of extinction P(t ) = = 0.43%. () 4. Discussion 8

9 The result (9), if we consider it typicl for other intelligent eings in the universe, cn explin the fmous Fermi Prdox [9]. According to our experience t the time x 0 civiliztion is prcticlly not oservle on cosmic scle, nd fter t = 70 yers is disppered. Our estimtes re in good greement with the rel threts to the existence of mnkind, chief mong which is the nucler wepons. It follows from () tht the estimte of the proility of nucler wr remrkly coincides with the dt of [0] otined y pulic survey - % over 5 yers, i. e. 0.4% per yer. However, tke into ccount tht we relly estimted only the integrl mount of R ~ ht, nd the vlue t itself ws received with the ssumption of the future stiliztion of h. Therefore, humnity cn extend the lifetime t, reducing its numers h y further reducing irth rte. Relted improvement of qulity of life nd popultion geing will reduce ggressivity nd therefore the likelihood of wr. This conclusion is consistent with the conclusions of the Mlthusin school []. Governments nd interntionl finncil nd economic orgniztions should recognize the new relity. Inevitle with decresing nd ging of the popultion reduction nd even cesstion of economic growth is good which will extend the existence of our civiliztion. References [] Doomsdy rgument, Wikipedi, [] As cited in []: Brndon Crter; McCre, W. H. (983). "The nthropic principle nd its implictions for iologicl evolution". Philosophicl Trnsctions of the Royl Society of London. A30 (5): doi:0.098/rst [3] Nick Bostrom (005), Self-Loction nd Oservtion Selection Theory, [4] World popultion estimtes, Wikipedi, 9

10 [5] Per Sjödin, Agnès E Sjöstrnd, Mttis Jkosson nd Michel G B Blum, "Resequencing dt provide no evidence for humn ottleneck in Afric during the penultimte glcil period" Mol Biol Evol (0) doi: 0.093/molev/mss06 [6] As cited in [4]: History Dtse of the Glol Environment. K. Klein Goldewijk nd G. vn Drecht, "HYDE 3.: Current nd historicl popultion nd lnd cover", in Eds. A. F. Bouwmn, T. Krm, nd K. Klein Goldewijk, "Integrted modelling of glol environmentl chnge. An overview of IMAGE.4", Netherlnds Environmentl Assessment Agency (MNP), Bilthoven, The Netherlnds. [7] Dt from United Ntions Deprtment of Economic nd Socil Affirs, Popultion Division, _FILES/_Popultion/WPP05_POP_F0 TOTAL_POPULATION_BOTH_S EXES.XLS [8] Projections of popultion growth, Wikipedi, [9] Fermi prdox, Wikipedi, [0] Jey Ulfelder, How Likely Is (Nucler) Wr Between the United Sttes nd Russi?, [] Mlthusinism, Wikipedi, 0