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# Class Note for ECE 449 at UA 3

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Date Created: 02/06/15

A I was 449549 Giantinnons System mutualitth World Dynamics In this lecture we shall apply the system dynamics modeling methodology to the problem of making predictions about the future of our planet Tl has been one of the most spectacular and also mo controv 3911 of all ap 1cations of this methodology repoited to this day Decemba 3 2003 start Presentation I was 449549 Glontinnnns System mutualitth Table of Contents Forrester s world model lSt modification reduce utilization of natural resources 0 2nd modi cation reduce pollution 3rd modification reduce death rate 0 4th modi cation simulate backward through time 0 5th modi cation optimize resource utilization Decembaquot 3 2003 start Presentation I we 449549 untinnons System whalingl Forrester s World Model In 1971 J W Forrester published a model that he had developed for the Club of Rome offering predictions about the future of our planet The model makes use of his system dynamics modeling methodology It is an extremely simple 5i 1order differential equation model He sold immediately several million copies of his book which was also quickly translated into many languages He was strongly criticized for his model by many of his colleagues Decembaquot 3 2003 Start Presentation lt2JEIgt I we 449549 Glontinnnns System mutualitth Selection of State Variables I Which variables should be used as state variables How many of those are needed There obviously is no good answer to these questions It takes either genius or recklessness to even come up with a meaningful answer Forrester decided that wrld population is a natural candidate to be chosen as an important state variable as the world approaches its limits to growth Another important variable is pollution as too much pollution will clearly have tremendous effects on the ecological balance of the globe Decembaquot 3 2003 Start Presentation ltnrgt A I we 449549 hummus System mutualitth Selection of State Variables II 0 A third good candidate is the amount of irrecoverable natural resources left In 1972 it may have require Vision to recognize that the exhaustion of fossil fuels will affect us in dramatic ways Today this is evident to us all 0 A fourth candidate is warld capital investment More investment means more wealth but also more pollution A fifth and final candidate is the percentage of capital invested in the agricultural sector We evidently need food and available capital can be invested in growing food Decembaquot 3 2003 start Presentation EA I we 449549 Glontinnnns System mutualitth Rate Variables and Laundry Lists I 0 Each state variable was given a single in ow and a single out ow rate except for the natural resources which are only depleted Let us look at the laundry list for the birth rate Forrester postulated that the birth rate depends on 0 It may make sense to postulate that the birth rate grows proportionally with the population thus start Presentation Decembaquot 3 2003 A I we 449549 ontinnons System mutualitth Rate Variables and Laundry Lists 11 0 Since functions of four variables are difficult to identify and at least call for many observations Forrester proposed a simplifying assumption each multivalued function can be represented as a product of singlevalued functions 0 This assumption certame is daring but so is the entire enterprise Decembaquot 3 2003 start Presentation EA I we 449549 Glontinnnns System mutualitth Smallsignal Behavior Forrester furthermore used a neat trick He defined the values of all variables in the year 1970 as normal took these normal values out asa parameter and formulated the functions as deviations from the norm With values in the vicinity of 10 0 He proceeded in similar ways With all laundry lists of all rate variables Decembaquot 3 2003 start Presentation A I we 449549 ontinnons System manslitml Statistical Year Books I 0 He then used statistical year books to propose sensible functional relationships for these factors 0 For example it is known that the birth rate in third world nations with a low living standard is higher than in more developed countries 0 Thus we could postulate a table such as Decembaquot 3 2003 start Presentation I we 449549 Gluntinuons System mutualitml Statistical Year Books II t 3mm mum cpum qur irm nu39n Imam Datum We gum am an mo Lao mu mu n mu m men ms 1 Lou m m mm Ll us an L50 M a 115 5 m t n 05 no 1 no u u um 10 31 DKMELIL cm DHMM NnMM QLM mu Ban1m nuke DenMJhu Balaton QuaLLi DJ L20 DJ L00 XI 2 a mu LG ma L0 L00 L00 LB 15 no r 17733131 DacM PCM qnc I m 015 La no mu m rzmwa m valh nu mammal outm QuaLLilz 75 Mg an 105 07 24 loo 3 CL39IIE 24 033 140 It 05 U 35 050 La mm Lquot 10 100 411 mu m rum mm 21 15 lids 45 050 30 v 3 quot 3955 s 0 Me 30 050 no 29 5 ms w u 30 070 L5 0 IL 7390 5398quot 35 910 39 39 40 059 m 03 025 aquot 3399 LS 032 M Mr 5u 1155 30 0 070 quotW 90 Decembaquot 3 2003 start Presentation I am 449549 continuous 53mm gunnng Statistical Year Books 111 In each table the leftmost column lists the independent variable whereas each of the other columns denotes one of the tabular lookup functions The top row lists the names of the functions Underneath is the name of the variable that is being in uenced by that table December 3 2003 Start Presentation ltIgt A 1215 449549 diontinnnus 5mm loheliugl Rate Equations Using these table lookup functions the rate equations can be formulated as follows Birth aze Population BRN A BRCM BRFM BRMM BRPM CIAF CIA m a CFIFR CIQR CIAFG CIAFT CIJisca rd CIDN Capitalln39vesiment CIGeneration CIGN v CIM 39 Population Death ate Population DRN DRC M DRFM DRMM DRPM Depletion Population 4 NRUN NRMM Pollution POLAT PGenerat139on Paprulation POLN POLCM PJbso rptiowL December 3 2003 Start Presentation ltIgt A I we 449549 ontinnons System mnaml Auxiliary Variables The following auxiliary variables are also being used CIRA EC IR FoodRatio MSL NRFR Pollut i0nRatio QLMF Qualityncfiife CIR Crowding Ratio H H Capitazjnuestmenz W CIAF m Population LanaLAs ea Popjenleoa m 10 CIAF NREM CIR v 1 CIAFN FPCI FCM 4 FPM E FN ECIR ECIRN Natural Resources NR1 Potlution POLS QLM QLF QLS QLC QLF QLM QLP CIR Decembaquot 3 2003 Start Presentation ltIJEIgt I we 449549 Glontinnnns System mutualiml Parameters and Initial Conditions BRN 004 nwmul birth rate CIAFN 03 our normalization CIAFT 150 CI1F time constant DRN 0023 normal death rate ECIRN 10 capital nwmulx zalion F0 10 food coefficient FN 10 food normalization POLN 10 normal pollution CIDN 0025 normal capital dimrd CI GN 0 05 na39rmal capital gcneratia39n anLArca 13510 l am of arable land NR 90 10 initial natural reauurcel NRUN 10 normal mama utilization PaLs 359991nquot mum1 pallufion P0174161st 265 normal population density QLS 10 standard quality of 12 The following parameters and initial conditions are being us ed Population 165 1o Pallu m 20 105 NaiuralReaou1ces 90 10u CapitalJnuestmeni 40 1Oa CIAF 02 Decembaquot 3 2003 Start Presentation lt2Igt NE 449549 Summons System Whalingl Overall World Model unruly ltgt cm 449549 Euntinuons System Whalind Equation Window El parameter parameter parameter paramet er paramet er Raramet parameter parameter parameter parameter paramet er paramet er parameter paramet er parameter parameter parameter parameter paramet er paramet er parameter paramet er Output Real Years Real Real mllutlclni lgtdlluudn rn 150D Real NatiResUutcai Unreedueraele natural resuurca 1n 19nd Real Capilnvesli quotCaprtal lnveetment 1n 190D Real GALE quotFr purtlnn dt eapltal luvestment 1n Bgrlculture 1n laudquot Real ER quotNclrmal blrtzh rate Real CIAFN quotCIAF numallzatlun Real CIAFT quotCIAF tune ednstant39 Real CIDN quotUrmal Capxtsl dreeardquot Real CIGN quotNclrmal Dapxtsl generatldnquot Real 3th drmal death rate Real ECIRN Caprtal nmnsllzs Emquot Real FC ddd mafixclent39 Real m ddd nermallzatld Real Landierea rea d arable landquot Real N39RI quotInltlal natural tes urcesquot Real NRU39N quotUrmal reeduree utlllzatl nquot Real pom quotNurmal mllutlunquot Real POLE quotStandard PUJJutlclnquot Real papdenenerm ndrmal pdpulatmn densltvquot Real QLS quotStandard quallty nt Jlfequot varlablee quotTulle 1n calendar Years ul H IEEI l ilZlil J l Inrtral Dundltlclns 2dr etat Papulstlnni arlablee a quotunrld papulstlcln 1n lampquot LL tnme e 19nd uid December 3 2003 Start Presentation lt1gt cm 449549 continuous system mmml Compilation 1351 Llcanse admlnlsczalzuz pmz Francnls Celllax and ms students Lxcansa number 1Dl m c Ealllez ClassesEce449EandlLb mecklng WuzldnudelJlnzldi chetk udal quotMarianoSe waxingquot check stazcad a mm 395 unknnwn scalar and 395 Scalar Equalzluns Check 0E WuzldmudelJlandil succgsszui zanslaca udal quotWazlduudsl unmiiquot amlaclan started mm 395 unknuhm scalar and 395 scalar Equalzluns u canscants mde Datamabe haunt varlablzs found expazlmanl SCDmea2CID u slmulace mlshed Plam39quotUualty7uf7L1feYquot l December 3 2003 Start Presentation A 1 I ma 449549 toutinuous System mammal Simulation Results I 5E9 Pupmauun lave yzays Pullulmn Iavslt Ears SEQ 2510 4E5 15m 359 2E9 U 1E9 19m 2mm 21m 19m 2mm 2mm E 2 souveesJevetrveers 0UaluygLLNayWeavs 1 35117 1 BE 1 7 a a 4E11 0 Ba 2511 1 190B 20m 2100 won zuuu mu December 3 2003 Start Presenta on A I we 449549 ontinnons System mutualitth Simulation Results 11 6E9 pmmmm mwea39 The model shows nicely the Emits to sea growth The population peaks at about the year 2020 with a little over 5 billion people 4E9 3E9 2E9 1E9 I900 2000 2100 N stural Resaurces evet ears 1 E12 W J BE 1 39 EEHr 4611 2E11 1900 2000 2100 Decembaquot 3 2003 start Presentation EAEE I we 449549 Glontinnnns System mutualitth 1St Modi cation 0 Forrester thus proposed to reduce the usage of the natural resources by a factor of 4 starting with the year 1970 0 This may be just as well The effect of this modification is approximately the same as saying that more resources are available than anticipated This is indeed true 0 Now the resource exhaustion won t be effective as a damping factor any longer Decembaquot 3 2003 start Presentation 10 l cote 449549 continuous System whalingl Program Modi cation I As we are now modifying a parameter NRUN this former m parameter had now to eaelmi w Unrecclverable natural resources In raun 1n 19cmquot peremeeex Reei Capilnvasci 4 nea quotCepnei investment m JSEIEI become a variable Fewer lee cm 2 Empenmn a capital nv estmenl 1n Bg39rnrultnzwe m near aneceee Parameter Rea ERNEI m Numal mth rete39 Parameter Real CIAFNEI 3 CIAF nemeiueemnquot c1 5 a quotCI 59 parameter Real PupidensinDInFZS 5 quotNurmal prulBLIDn denelcy parameter Rea 9151 1 Standard queim e foe Output v labia Haul ad parameters Real RUN Normal rasclurce uunzeuen equatlnn Years Lune 19m Parameter Equatlu I had to extend a few of the fnnctron domains gggggmlimggj gigg ag 3R to prevent the mert clauses in the Ptecewtse 25 else 1 n on function from killing the simulation December 3 2003 start Presentation lt11 gt A lam 449549 nntinunus 93mm Whalingl Simulation Results 111 Bngugulatmn tewryears E T Pollution lemmast 559 1 SE11 Aa 1E11e 3E9e 551n 2E9 159 Equot U l 1 l 1 l 5E1D 1 1 1 1 1 1920 1960 2mm 2040 men 1920 19511 man 2041 men NatumLReawvces lemmas 12 DualityiuLLile yyear5 951w B 8E11e 7E11 439 6E11 0 1920 1950 2mm 2040 men 1921 19m 2mm 2mm man December 3 2003 start Presentation lt19 11 A I we 4495491Glontinnunx 91mm lohelingl Simulation Results IV EB Pupulatmn tavernears PnHutmn reveweays ZE H 155117 497 1E 7 3E97 55m 2597 19 Equot n 5E1 n v 1920 men znnn 204D zuan 192m 195m 2mm 2mm 2mm This time around the population peaks around the year 2035 at a level of approximately 58 billion people Thereafter the population declines rapidly in a massive dieoff The natural resources are not depleted until after the year 2100 December 3 2003 Start Presentation AA I was 449 549 m nnnux System mmml 211d Modi cation Forrester thus proposed to additionally reduce the production of pollution by a factor of 4 starting with the year 1970 o This may not be as reaSOnable an assumption Yet at least in the industrialized nations a lot has been done in recent years to clean up the lakes and reduce air pollution Now the pollution factor won t be effective as a population killer any longer December 3 2003 Start Presentation 12 A I we 449549 ontinnons System mutualitth Program Modi cation II 0 As we are now modifying another parameter POLN this former parameter must now also become a variable Hr 0039000000000 Mampulated parameters Real RUN quotMammal resource utilizationquot Real POT quotMammal pollution A equation years a time 1900 Parameter equations RUN if years gt 1370 then H259152 1 U NLqu InPnrtZ slgnalu NRUN POI I if years gt 1970 than D 25 else 1 I Pulinum IantZ slgnalUl POL Decembaquot 3 2003 start Presentation I we 449549 Glontinnnns System mutualitth Simulation Results V HEB Pnpulehun levelyeats 6E9 Penunon level ears 5E9 459 4E9 zeae 2E9 0 0 t 1000 2000 2100 1900 2000 2100 1 ET 2 N nnramesmes tetextvee m Guahlyiufiufe yyears we A Bar 0 a BEHe 0 5 1900 2000 2100 1900 2000 2100 Decembaquot 3 2003 start Presentation l3 A we 449549 untinnons System whalingl Discussion I This is where Forrester s book ends He plotted the population curve on a double page stipulating though he never wrote so explicitly that this is what we need to do to overcome the hump problem Evidently this conclusion is erroneous If we look at the natural resources we see that by 2100 they have again depleted to a level where the population curb will Set in Let us simulate further 8E9 Pupulanun lsvalyaars 6E9 2E9 7 19m ZDDU 210m 2200 2300 24mm 260D Decembaquot 3 2003 Start Presentation lt2JEIgt A we 449549 Glontinnnns System whalingl Discussion 11 The results are very similar to those of the original model except that the population now had a chance to climb to almost 8 billion people before declining again and that the hump takes place 80 years later This by itself is not unreasonable Forrester is saving the planet one day at a time and his attention span is certainly longer than that of most politicians who aren t interested in saving the world beyond the next election date Decembaquot 3 2003 Start Presentation ltnrgt 14 A it 449549ztliontinunus system manual Hindsight is Always 2020 Since Forrester developed his world model more than 30 years have passed It thus makes sense to compare his predictions with the meanwhile observed reality Forrester s World model 7 comparison of scenarios x 6 a 1n ummm World population w in 5 1900 1920 1940 1960 1930 2000 Time years December 3 2003 11ml Start Presentation Aquot it 449549 00110111101111 99m latitudinal Program Modi cation III The reality is far worse than Forrester s worst nightmare The world population grows much faster than he had predicted Forrester had not taken into account the amazing progress of medicine People live longer than ever before at least in most parts of the world in Russia they now die 10 years younger than during Soviet times and in Southern Africa they die as early as never before due to AIDS and the infant mortality is at an all tirne low To accommodate for this progress let us reduce the death rate in 1970 from 0028 to 002 December 3 2003 Start Presentation A I we 449549 ontinnons System mutualitth Simulation Results VI Populamn leveuyeare Papilrteast years 7E9 BES rv SE9 7 4E9 e 3E8 2E9 e 7 1 E9 y 1900 1920 1540 1550 1980 2000 The t is now reasonably good Let us check What this modification does to the longerterm simulation Decembaquot 3 2003 start Presentation EASE I we 449549 Glontinnnns System mutualitth Discussion 111 1E1 Pnpntamn Ievel vearsj aEae 6E9 4E9 2E9 0 t y t y 1900 2000 2100 2200 2300 2400 2500 0 Not much has changed in the longer run The population rises now to approximately 8 billion people before decaying again down to the same 2 billion people in steady state that all of the other simulations have shown Decembaquot 3 2003 start Presentation u l we 449549 mttnunus System mammal Model Validation Let us discuss how we may be able to validate or disprove the model One neat trick is to simulate backward in time beyond 1900 Since we know the past we may be able to conclude something about the validity of the model Simulation backward through time can be accomplished by placing a minus sign in front of every state equation If all time derivatives have reversed signs the same trajectories are generated but the ow of time is now reversed December 3 2003 Start Presentation A l 449549 untinuuu p tml mammal A New Level Block 0 To this end a new reverse level block was introduced 539 ll Mll rim 3 name W t R am RE H mm Rem m f sl1 L1 cur 2 19nal1 0 gnu derLlevel 1f lave gt m then d1rquotrate n r rateiout else El g f Declarations of clas 1 The brown levels contain a variable dir When dir 1 the direction of time ow is positive when dir 1 it is reversed 0 l furthermore introduced a minimum level xm which ensures that eg none of the state variables of the world model can ever become negative December 3 2003 movwlutgi jm r w Start Presentation l7 A a Wm 449549 Continuous ystem musling Program Modi cation IV Eanammn Depienan u unamy A wz 449549 Summons 3th Mbelittn Program Modi cation IV 2 ALIle parameter Real 0L51 n Standald qualnv Di hie 1 Output varxablas Real Vearsstarl19 39Tnue m eaieauax years x Manipulated paramecas Rea 1mm Nurmel reseuree umiazauen Real POI Nmmsl Pollutlm Rea mm quotwermai death rate Measuremem date Real Uneivals12lg lgl 192DISSDJSQDJQSD196D97DlSBD199 Z DEI 7nE56e A 3731295 19n3e95 395223629 Real Pummeas 2510 Real pup vels121 ses1 75e91 ase92 o7es2 3e92 ssse93 nasaea 3 Reveslhle Lune new Real 1r Parameter Reai unereverseezuu Tlme of tune reversal equal un Parameter Equatlms RUN 1f years gt 197m men n 25 eise 1 n 7 1mm Peijera IanLZ S19nal1 I m years gt 197a Lhen 1 n2 eise n ma DRinmm InPDtLZ SlgnalU mm Measurement date Pepjeas e SVSLEniDynEmlcs Interfaces Plecewlsexveaxs xigrldglnneivals yegnawupgais Reversible Lune flaw Cline me reverse men 4 eise 1 e d a r e dlr Capltaliluvescment dlr e dlr CIAF cur dar darVEats cur Start Presentation Declavemnns nfciass A I we 449549 ontinnons System mutualitth Simulation Results VII 5E9 4E8 3E9 l 2E9 1 E9 7 1 PuHuuan levavears PoHHtwn Exmews Pnuumn FkalLyaars Fnhnnmx may aw El x x 19m 1920 1940 1960 193D 2DDEI 202m 2040 2060 anm 210D I first simulated forward through time during 200 years then reversed the ow The reversal worked well for about 16 years after which the trajectories separate I superposed another simulation where I simulated forward during 150 years then backward again The trajectories separate after 18 years Decembaquot 3 2003 Start Presentation lt2JEIgt A I we 449549 Glontinnnns System mutualitth Discussion IV The simulation is numerically unstable in the backward direction The culprit is the pollution absorption equation The tiniest deviation from the correct trajectory leads to an exponentially increasing error Special stabilization techniques are needed to simulate backward through time A discussion of those is beyond the scope of this class One possible algorithm varies the initial pollution value at each integration step such that the sensitivity of the solution to the initial value is minimized Decembaquot 3 2003 Start Presentation ltnrgt l9 A i GEM 449549 Summons 91mm mammal Simulation Results VIII The results shown below are for a simulation forward in time over 30 years then backward in time over 37 years x 1 09 Forrester s World model 7 Simulation backward through time 22 World population M to m a m 1 7 1 a 1890 1395 1900 1905 1910 1915 1920 1925 1930 Time years December 3 2003 Ira Statpresema m lt11 gt y i 449549 uutinuuus y tau mam Discussion V The simulation suggests that the world population was declining before 1900 reaching aminirnum around 1904 We know that this is totally incorrect So how can we hope to simulate correctly until the year 2500 Evidently we cannot We shall see however what valid conclusions can still be drawn from the model December 3 2003 start Presentation 3 EQL AEQ 39 ELL lt19 20 A was 449549 Gluntinuuux System mnamgl Optimization 0 Let us now return to the model after the first modi cation 0 We want to optimize the consumption of natural resources after the year 1970 0 To this end we shall need a performance index What is good is a high value o the minimal quality of life after the year 2000 optimizing the past doesn t make much sense What is bad is ardieoff of the population 0 Accordingly we modify the program once more This is all done in the equation window December 3 2003 Start Presentation A I we 449549 Ginntinuons 51mm mammal Program Modi cation V r a 7 7 AEULI are Al Real years Tlme 1n ealendar Yearsquot Manlpulsted parameters Real NRUN quotNormal reeeuree utillzstionquot parameter Real NRUN21 u quotReeeuree utllizatlan after 1971 Optlmlzatlan Real relidPDp quotRelatlve derivstlva of DDpulstlonquot Real mlnichlp quotHlnimsl derlvatlve or DDpulatlonquot Real nunch startl quotMinlmum quality at llfequot Real PerfiIndeII quotPreformance indexquot A equatraa years a time 19m Parameter equstlans NRUN 1 Year gt 197D than NRUNz else 1 u NRinclrm Inperr2slgnal1 NRUN Optlmlzatlon relidPop BrrehiRaee rate 7 DeaehiRaceracePepulatlen level when eampleltluu1 than mlnidPCIlJ m1n 1313m1n7dP012 relidPap dnlnEQl m1n Drem1n7QI Qualltyiofillfe y PerfiIndeII millain 5m1n7dFDp a f December 3 2003 Start Presentation lt1Egt 21 A I we 449549 ontinnons System mutualitth Simulation Results IX H ex ears an I E 39ear39s E H ex Ears H EM ears NRUNZ 025 NRUNZ 15 NRUNZ 075 NRUNZ 1 NRUNZ 15 152D 1950 2UUEI ZUAU ZDBD 212B 21 EU 220D The first two simulations are plagued by massive die017 The others are fine 0 Yet in the short run those solutions that Will give us bad performance dieoff exhibit the best performance Decembaquot 3 2003 start Presentation EASE we 449549 Glontinnnns System mutualitth Discussion VI Politicians have a tendency to focus on shortterm performance Their attention span usually ends With the next election date 0 Consequently they Will most likely favor a solution that Will lead to a massive di eD further down the line apr s moi le d lugel Decembaquot 3 2003 start Presentation 22 A we 449549 untinnons System mnaml Conclusions I 0 So what can we conclude from this model 0 The answer is simple We need to perform a sensitivity analysis to determine which answers are least sensitive to both the overt and the hidden assumptions made in the model 0 All simulations show that the limits to growth are imminent For the rst time in recorded history for the first time even since Adam and Eve were expelled from paradise because the devil the Great Innovator the who maximizes entropy seduced them to becoming smart and smartness comes at a price inte jgent beings are expected to assume responsibility for their actions Earth is proceeding from a system with unlimited resources to one that is resource limited Decembaquot 3 2003 start Presentation EA I we 449549 Glontinnnns System mutualitth Conclusions 11 0 Hence we need to take the entire food and fresh water that Earth can produce and divide these resources into the number of people There is not one fixed equilibrium We can either live in smaller numbers well or in larger numbers with hunger One would hope that being intelligent mankind would opt for the former solution Yet there is little evidence to this effect and much evidence to the contrary It seems that our intelligence only helps us in a local context In a global setting we behave not much different from lab rats except that we are aware that this is what we are doing whereas lab rats are not Decembaquot 3 2003 start Presentation 23 A I we 449549 untinnons System mutualitth Conclusions 111 Our at economy has made us believe that all problems can be solved by printing more money Yet money cannot be eaten Ultimately someone has to grow the food that we are eating By burning fossil fuels we are using resources that we have not produced It is like spending money that we won in the lottery Once the fossil fuels are gone we will have to produce everything that we spend A given number of people can only produce a fixed amount of goods Decembaquot 3 2003 Start Presentation lt2JEIgt A I we 449549 Glontinnnns System mutualitth Conclusions IV If Earth can carry well a certain number of people in steady state and if this number is smaller than the current population which may well be the case Forrester s model suggests roughly 2 billion people but this number may not be entirely correct though it won t be Very far off then it doesn t help to design mechanisms that will ensure that the population can grow further over a short period of time This only means that it will have to come down again later and may do so violently massive die0m Yet our politicians will do everything in their power to keep the GNP growing for a few more years which can only be accomplished with a larger population Decembaquot 3 2003 Start Presentation ltnrgt 24 A I we 449549 ontinnons System mnemgl Conclusions V 0 More people means more tax payers More people also means a younger population ie more people contributing to the social security 0 Yet more people also means a larger decline later It also means an increase in the feedback gains Which implies a destabilization ie an increased risk of massive dieo Will humanity be smart or Will we be greedy We are most certainly liVing in interesting times Decembaquot 3 2003 start Presentation EAL we 449549 Glontinnnns System mutualitth References Cellier FE 1991 Continuous System Modeling SpringerVerlag New York Chapter 11 Forrester JW 1971 World Dynamics WrightAllen Press Cambridge Mass Cellier FE 2002 The Dvmola System Dynamics Library Cellier FE 2001 The Dymola WorldModel Decembaquot 3 2003 start Presentation 25 A I we 449549 ontinnons System muslingl Interesting Websites I 0 Magoon LB 1999 Are we running out of oil United States Geological Survey USGS httpwwwecearizonaeduNcelliertemporarvUSGSpdf le loads slowly download recommended 0 Puplava J 2002 Hubbert s peak amp the economics of oil Financial Sense online httpwww nancialsensecomseries3paltl htm 0 Campbell CJ 2002 Peak oil an outlook on crude oil depletion MBendi InformationforAfrica httpwww mbendicoZaindvoilqp0070 htm Decembaquot 3 2003 Start Presentation I we 449549 Glontinnnns System muslingl Interesting Webs1tes II 0 Tietenberg T and W van Dieren 1995 Limits to growth A report to the Club of Rome httpwwwdieo 39orgpage25htm 0 Bartlett AA 1998 Re ections on sustainability population growth and the environment Renewable Resources Journal 154 pp 6 7 23 httpwwwdieofforgpage146htm 0 Thompson B 2002 The oil crash and you Running on Empty httpwww runningonemptvorgoilcrashhtm Decemb 339 2003 Start Presentation 26

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