William A. Dembski and Robert J. Marks II, "Life's Conservation Law: Why Darwinian Evolution Cannot Create Biological Information" in Bruce Gordon and William Dembski, editors, The Nature of Nature (Wilmington, Del.: ISI Books, 2011) pp.360-399
E F E IS an irn:volcaIJ!e selection and exclusion. as when you marry one woman you up all the so when you take one course of action you up all the other courses."4 Intelligence creates information. Bur is the causal power of Darwin's main claim to fame is that he is supposed to have a that could create informa- tion without the need intelligence. Interestingly, he to this mechanism as "natural selection." Sel.e~tion, as understood before had been an activity confined to intelligent agents. Darwll1 s great coup was to the power to nature-hence "natural selection." as conceived Darwin and his acts without is non-teleo- and therefore unintelligent. As genetlClst Coyne puts it in opposing intdlige:nt "If we're to defend we must defend it as a science: a in which the of life results from the action natural selection and on random mutations."5 But do and Darwinists insist that to count as must be non-teleological?6 did that rule come from? The of with the sciences is itselfa well-established science-it's called engineering. conceived, to the engi- ne.:::nng SCIences. 1. THE CREATION OF INFORMATION But to return to the at does nature really possess the power to select and th,>rph" create To answer this we to turn to relation between po~,sit)ilil:ies to create inlonnal:1011. intelligence rpcm 1rp< 0'-<11'-',1W';; act matter ~nd The matter-information distinction is old and was understood by pn:cedLng sentence illustrates very the ancient For them, was matter, or inert to be arr'ange1d; sequences. Most such sequences are gitlbeTish (11llj)r01nO,ull,ceable a'rrang;enleIlts and there was information, active stuff that did arranging.7 distinction provides a mc~anjnl~lu.1, ters). Ofthose which are useful way of up and sense world. Left it is uncontro- to most have nothing do with information versial. it becomes controversial once we another dimension to it, that of ellmlnatlng vast this space we sw:ct:eu locatinlg the first senten,ce LH~l"'lllanguage.Each nature and paper, theTdlY c;re;wrlg sentence in the inlorrna't1on-~;enera.tlI1lg reduction of POSSlOIllU':::S act. Together, these redlucltiollS constitute a search that ide:ntihc:s one lJU,,,,UJllllY first sentence this to the sion of Information to the exclusion of others. Unless ex.:lude.d, no To say raining or it's not mative because it On the other to say "it's rainirl~( exc;lU
thl-oUlgh powers external to it-a de:signiflg il1telll!2;eflCe rUDlVLJiC and ancient Stoics with immanent tel lIdlWldllOlJL!, natural causes about causes but are not On non-lte1c;ol,ogi.cal natural causes, ultirrlat1e1y attraction and rq:lUl:SlO:l1. The pal'ticul2lr, is to show that ogy. In trallslatlOllS have in not techne is "art" but shuffled around Nature is a matrix for eXlprt~Sslng existent information. But the ultimate source of that information in an intelli- gence not reducible to nature. The Law which we m paper, that is case. not Darwinian or even role as an immediate efficient cause in the law shows Darwinian evolution is it inherent in Darwinian evolution is sci,enti±lI:aLly asce:rt21inabJle--it it had the cap'acllty INFORMATION PROBLEM here translated root me:aning pnJdlll0:S information not m the de'vehJDin2: inl:orm2ltlcmaJly rich structures from hi"I""'T is a science of inl:orm,l- the Cap,aCltleS that to be m±OrnllarlOn to uncien;tarldulg life Prize winner Manfred of "13 l:$JOII0g1StS SfU.p-ouuumg is not the wood that makes up a :::'Z8lthlU8Jry have ex~)llcltly information at the center selltenCi:-lll1a.lnlllg is not in the letters of out eV(Jluxic)ilclry h,r,I",[Jov' "A central in contemporary is that statw:-lll1a]nlllg is not in the stone out ofwhich mtonnatlO.n. LJevelclpnJerltal h,n,l"o'v can be seen as the of how information in the statues are Each de:;lgller. So too, the design genome IS lldU'ldll;U structure, and eV'::llultlC)fi,lry n",l"au how COlltelllds that the art that constitutes life. Instead, came to be there in lllC:-llldKJlll') requlfl:s a de'llgrler. Given the the obvious questlon issue in the debate over and evolution alive it must be suiltalJlv struct:ur,ed. stated as follows: Is nature all the resources 0f!2;arllsln is not a mere matter. and what makes it it about the structures we see us, or does ter 1S into very forms. In other nature also some contribution of to about those structures? Darwinian Where did information necessary for life come naltura1i:sm argues that nature is able to create all its own information and is therefore cOJnp,lete. emergence of life constitutes a revolution contrast, argues that nature is to re-express informa- rates the from the and m±onuanon. The in your and the illi:01up,!et:eness seems to presuppose a distinction that matter-the inl:orma,ticm--clitJ-ers inl:elligc:nt causes be natural? As the sci- causes operate ao:ol:dJng to deterministic nO:l1dc:tel'mlllll:>tlC laws dl:ara.ctc:n,~edin terms and their THE information problem is to determine WfletJler IS to cornplement from a lifeless Earth over the course ofnatural life forms that ev(:ntually natural forces in the origin and sul)sequent developme~nt evolve into human who then write economic treatises like Das II-t,pt,'UL. But can we determine nature has what it Within Darwinian lldlU.ldll"Jll, pnnClpal.!y natural selectIOn on ran commonness of life on Earth tends to lull us into comr)la(:erlcy, valnatl0flS, control the ev()lutlo:nar'y may out of eV'orVWllere, But there was a time when the Earth contained no mlJltlce:lled o,rg:miSIT1S that process but play no role in or controlling it. ~Hl,"l,e-l;elJ.eu the Earth contained no life at not even Theistic evolutionists attempt to make room for God within this Darwinian scheme ,~U, there was no Earth at no Sun or Moon or sister pu"",,CO, U"CH.. claJITung that God the universe so that Darwinian processes would produce living there was a time when there were no stars or >;"'''''''....0 about the natural that things makes sure not to those forces once are in Though logically possible, theistic evolution offers no reason for that nature is a divine creation. :'luppose we go back to moment. Given the ofthe universe since we As Francisco Ayala put it, "It was greatest accomplishment to show that the direc- say-m retrospec:t--that all the pO:,SltH1l1tleS forms like us were in tive of can be explained as the result of a natural process, natural sense present at pOSSible statues are in some sel,eCl:lO:n, without any need to resort m a Creamr or external "17 Darwinian present in a block unIverse, galaxies and stars eve~nt;Ja!ly far from a creator is with a natural world that is entwelv "v"'u.... u, then life as complicated 'W~'PTlhpr us. But that still doesn't tell us how we got here or sUl:hc]eru creative Theistic eV()lutlOl11sts think Darwin got nature and then adapt their theology to to produce us apart design. Nature DfCwj(jes COllC1JtJo,n for our existence. suit Darwinian science. of intelligent contrast, ask the logically question is it a suthClent .... Vl'U"UVIL qwestJ:on whether Darwin in fact get nature right. we think natu- As Rolston out, are not present in pn:mlf11re apart from have the power to create biological information? single-celled organisms in the same way that an oak tree present in an acorn. atl:en:lplted to resolve this providing a naturalistic mechanism (natural oak tree unfolds in a or way an acorn. But the same cannot be on random that account the production of for the at one end and humans Some of Darwin's to'llowers consider this mechanism so that it makes unneces- sary any intelligence Dawkins even went so far as to state, made it to be an fulfilled atheist."18 like Francis Collins, think that an the Christian set up the conditions that make it possl!ble for the Darwinian information. acc:on::Ulllg to to assert that nature possesses the '-"HUHJ, "makes it for the scientist-believer to Int,eHectuaHy tUlhlle~d and spu'ltually causal powers science has the of demonstrating alive."19 Yet for Collins and hand is nowhere evident in the wtletJtler nature possess such causal powers. Mon:mrer, we do not luxury, ev,ollltH)ll,lry process. Atheistic and theistic evolution hands in that purpose- like Aristotle and many ancient that life and the universe always in is sci/mt,lftc,atL) 20 Aclvances m and Earth has not How does the Darwinian mechanism intelligence in its account ofbiological infor- Earth was a rendered it Yet some- mation? Richard uses an to illustrate how the Darwinian requmng mechanism apart from intelligence. 21 For convenience, we "('trvl"r of Int,JrITlatl'Jn-:rJch blOma,cromoleCll1es eme:rged. How did refer to this WEASEL. He starts with the target sequence: METHINKS~IT~IS~LIKE~A~WEASEL 3. THE Note that he considers Roman letters and spaces, spaces reIJreseJ:lte,d here bul- Karl Marx is said to have that the rwenrV-SIX for lets--tnus, twenty-seven possibilities at each location in a that is tw'entv.. el~~nt 16 suc:ce~;Srll1, world. Yet to be Left characters in ~ ~~~ m tried to attain this target sequence rallldoluly shak power to transform into Marx's Das Kapital. Marx the of the alphabet, it on howe:ver, do that power. But that raises the how Marx U",.uo....u to From a Darwinian any such as results from a and process. without the need of any llltelllge:nce, starts off To genet'atc the m target sequence, pure is simply not rithm was to create the target sequence up to the task. was in fact into the aJ~;or'idlm from the start. The Darwinian ifit is to Now the of the Darwinian mc:challlsm possess the power to create cannot veil and then unveil existing to circumvent the limitations of pure chance, information. it must create information from scratch. '-""d,'UY. UlwkillS'S consIders the Start out rithm does ofthe sort. of Roman letters and spaces, e.g., Dawkins uses a search to illustrate the power Darwinian he denies that this as it operates in biological evolution (and WDL~MNLT~DTJBKWIRZREZLMQCO~P thus outside a computer constitutes a targeted search. after his METHINKS·IT-IS·LIKE-A"WEASEL he adds: "Life isn't like that. lnijlvldllalletters and spaces in the current sequence; those £'VOlllt1Cm has no goal. There is no long-distant target, no final to serve sequences that match more letters in the target sequence, dl,;carding the rest, This as a criterion selection."24 Dawkins here to two equally and relevant ex(~mphhes the Darwinian mechanism: step to the random variatic'ns HULUld,Ui y constructed patterns that we arbitrarily raw for process; step the selection 111l:enests, and targets as patterns that exist inde- variants that are better fitted to their environment letter sequences and interests. In other can match the target sequence more outsi,de) or intrinsic (i.e., inherent in very order this converges to Dawkins's target sequence. which Wtltc)';m.ak,?r he summarizes a run the that in a mere rOI'tv··three programmers COl:lVe:r2:<~d to the target secluenc;~:"j attempt to solve of their choice and living forms have come about without our choice or No human has biological targets on (1) WDL5MNLT5DTJBKWIRZREZLMQC05P nature. But fact that can be alive and functional in certain ways not in oth- lndlc:at,es that nature sets her own targets. The targets we say, are "natural (2) WDLTMNLT5DTJBSWIRZREZLMQCO~P a term from There are so many ways matter can be conhgu:red to be alive once so many ways it can configured to serve different bIC)10JglCaJ hlnC;tlCms, Most of the ways open to as well as bic)loj2;ical (10) MDLDMNLS~ITJISWHRZREZ@MECS@P are dead ends. Evolution may be as the alternative "live ends." In other survival and set the targets Dawkins's IS a tal:geted search after all. COMPUTATIONAL VS. BIOLOGICAL EVOLUTION (30) METHINGS@IT@ISWLIKEeB~WECSEL the known phYSIcal Ull,lVel~e, eleme'nts that can be sampled queried) from a limited. At the time this writing, the computer is the $1j:)-tllllJI0n sUlper'comj:mt,er at Los operates at 1.059 per 25 If we size 1, then physical universe 12 billion years), be search space. It is estimated that the of tries on average for pure chance to the target sequence, orl';anlsmls, both sm!?:le-celled millltlCeHed, that have existed on the Earth over enlDlovin2 the Darwinian mechanism it now takes on average less than one hUlllcired billion years) is m = take a million Roadrunner pn)dllCe it. In a for pure chance becomes enlinLently rUJl1nimg the duration the universe to as many "life events" as have the Darwinian mi~dlanlisrn, So does Dawkins's ev()lutiona:ry algontJ::lm Chapter, we treat m as the upper limit on the number ofelements that a anism to create bic)lo,gicaJ or query. Is there an upper such upper From examin- outcome UlwkitlS cOJmput~lticlllal ca!Jaclty of the at theorist is the number that the observ- THE able universe could have its entire mllltJlbljlllCm-ye~lf 27 computer to achieve any result want. Take ml:elJJg,:nt the limit on the number of elements that a critic Robert Pennock's work on the computer program AVIDA. AVIDA, written , which sets an absolute limit on the size search. uses to evolve certain types of which are viewed as virtual Most search spaces that come up in the formation of are far too V1';d.l"~111'. From the program, Pennock infers that evolutionary processes to be searched Take the for a very modest one that say, operanulg in nature can produce complex 32 Yet other computer programs, hundJred amino acids in are several hundreds of amino acids in such as suggest that natural selection will have difficulty evolving features that need . The space of all sequences are one amino acids to form simultaneously for selective advantage. From MESA, Pennock might just as well have has size 1.27 x , which exceeds limit. For ml:en:ed that certain types of biological (such as Michael Behe's irreducibly com- a via blind search to a molecular machines) may be unevolvable Darwinian means.33 So which program gives Exhaustlv,elyor size to find a target this the better into which seems w it, or not present cOJmFlUtatlonal ClpclCllJeS also the cOlnputanonal CaF,aCltleS which seems to disconfirm it? verse as we know it. It's in measure computer programs can be to prove any evolu- Biochemist Robert Sauer has used a known as cassette to determJ.ne result one wants that ICAM was the Institute Complex 34 much variation can tolerate in their amino acids without His Aclaj:,tnre Matter. Its mission is to real-world material systems (as opposed to results show that this variation into account raises the a 1aO-sub- sllllCOn-'l'Io.rld. virtual become complex and Talk to most working biologists, unit to m . But atoms in our is still and will tell you computer do not shed much light on actual biological vaJlisl1ingly small. Add to this that most are not 100 but 250 to 300 amino acids in evolution. Richard Pennock's collaborator on can appreciate this point. and also that most exist and operate in proteins, Lenski is known not for his work on computer programs that simulate biological and any prospect blind search space 28 rather his work as a conventional biologist to evolve populations l'ornm );<:;][1<:;1,'-1, it is impossible or impracticable to test about evolution in a par- tion organisms meet, mate, mutate, and Sandra Blakeslee, by the deliberate setting up with living organisms of for the New York Times, the results under the headline "Computer 'Life Form' We can attempt to partially get around this by constructing [computer] Mutates in an Evolution Natural Selection is Found at Work in a Digital reF)re~;enting the system we wish to and use these to test at least the World." Natural selection found at work? I suppose so, for as Blakeslee observes with our ideas."3o Or as Heinz Pagels summarized the matter two decades solemn incomprehension, "the creatures mutated but showed only modest increases in "The way to see evolution in action is to make computer " because "in real cOlmp,Je:x:ity" Which is to say, they showed of interest at all. This is natural selec- time these changes take aeons, and IS "31 tion at but it is hardly work that has worked to intended effect. 39 In the last two that elucidates bio- eV;Jlu.t1c,n has waned. is that? The short answer is that programmers can cook Berlinski raises here an does mean for rej:,!ication, and mutation-iutact. Where the information "comes from" is, in from of Darwinian evolution to succeed? For proponents of the selective process itself.43 that the and sur1posed to have dlsipla'ved passage is remarkable for what it seems to The details sinrm!latilon are not here. We have elsewhere that ev is not as free lllireStlgatc)r interference as Miller makes out.44 But let's grant, for the sake of argument, that Miller is in interference with the of the program. His claim that the information comes from the selective process is then correct context, Miller suggests ev, and evolution in outputs more infor- mation than it In selective processes as much infDrmation from the start as output at the end. In ev, for the selective process in!JU1:te,d information in the form of a that served as a fitness 45 programrrlers to talthhll!y measure. instead of information in the sense it from "Ll"U_U, yet, deg;rades e:X:lstlllg lnltofmat:lOn eV(J!uLt1C)llclry processes pnJc!llce it the much weaker sense )'HUlin i 0 n evolution dismiss eXl.stlng information. blC)!o.glC:alJy n~le'varlt information reflects a failure of The view that cannot create information shuffle it around is programs to capture bic,lol?,ical Darwinian turn this standlmg and well-established. Over years ago, Leon a III mlurlma.trcm criticism books do Darwinists get their programs made that very "The machine does not create any new inJ:orm,ui()n, claim these programs fail but it pertclrnls a very valuable transformation of known m!rorm;Ul()n. bl010j2~ISt Peter Medawar made the same in the 1980s: "No process iCclUJCU an there is a way forward in no mere act of or COmfJut:er··progralnrnalble oper2ltlC)fi--C;an cornmon, nalne!y, that IS pm,slble content of the axioms and or observation statements from which it nrl.rf'Prll< "47 processes it had better To see that Darwinian processes in the weaker sense m~ltherrlatlCa!!yifit is constitute an exact science.42 Yet the common pre- pf(:-exi~;tirlginj~orm~lti()n rather than the stronger sense it from need ICl rUl1n 1Oln processes be raises a log;lCa.lly me:asunng the information processes. This we have pro- questlOll. We have considered whether models Darwinian evolu- the literature.48 Yet basic blC,loi~lc;ll systems. Some appear Dawkins's WEASEL. What allowed his evo,lutlon;ary a!g()nthm to converge so METHINKS"IT"IS"LIKE@AeWEASEL result. But the IS willetiler, is that a fitness function was embedded in the alg.onthIll m2lthl~mat1cal and in what sense, models of processes allow the pnJdllction of VUULLU, the very target was itselfstored in the But in that case, fitness func- blOlloi~lCcll!y relevant at The ofthis paper takes up this qu<~st1on. tions galJglng distance from any other letters and spaces could as have sulJstituted for the one Dawkins and with those fitness the a!gonthrll 5. ACTIVE INFORMATION could have on any sequence whatsoever. So the target sequence METHINKS*IT@IS"LIKE@A@WEASEL had very small in Thomas Schneider's work on the computer simulation ev, (rougJl1ly 1 in pure chance from a query; and it has attempts to account for the apparent increase in information that results from that alg;oflthm. to 1) of from Dawkins's in a few dozen LlUl:nt;~. "W/'-._~'_ needed to drive this increase?" he asks. three and But that a fitness function that gauges distance mutation." He contlnules, sequence, and such a fitness function can on any sequence of twentv-eH?:nt letters and spaces not on So how many Where's the new information IS it into fitness functions exist? . And what's the Dawkins's the system at the statt? No chance since the sequences are ran- fitness function (which gauges distance from among domized. there's hidden information in the program itself? Not Schneider all these other fitness functions? 1 in made the source code ofhis program open for and there isn't even a hint without structures on this space of fitness tUllCtlOllS of such nonsense. Did Schneider the parameters of the program to get the results he ifsuch structures exist in the and constrain the choice fitness lunCitJons, where wanted? Not at In the program in about any way still results an did that information come this space increase in measurable so as we those three elem"nts--st:lec:tic)n, or associated with Dawkins's THE evolutionary algorithm finding the target sequence q in ofp) is offset by undel'IYlng search space Q to locate the target T. \)I.!e then define the exogenous mforr.rtatlOn improbability offinding the fitness gauges dls;ta11ce from that sequence (i.e., p). Is as -log(q), which measures the of alternative search 5 in locating the target Dawkins's far from how could T. And we define the active 1+ as the difference between be with probability, raises the new how one overcomes the and exogenous information: 1+ =: In-Is =: Active information therefore measures the low offinding right fitness for his Dawkins has thus information that must be added the sign in on top of a null search to raise an one hole another.49 alternative search's ofsuccess a factor of Simulations such as Dawkins's Adami's and Schneider's Dawkins's Adami's and Schneider's ev are alternative ev appear to support Darwinian but for lack of dear that searches. As improve on a null search the of successfully track the information into them. These programs on of loc:atlng targets. information-theoretic terms, these In with The information works. The hidden in them can be uncovered a we endo,gellOtlS information is indicating the extreme the target with call active Active is to what the balance sheet the blind or null The exogenous information by contrast, is much smaller (possibly is to financial as the balance sheet track of credits and so active In(ilcatlng the relative ease of the target with an alternative search S. In replac information track of and outputs of sure that receIve with these simulations fail to account for the in these In other their proper due. Information does not magically materialize. It can be fail to account for the active information or can be around natural forces. But natural and Darwinian processes in n~'·;-1r'"I·,r do not create Active information us to see this is the case. 6. THREE CONSERVATION OF INFORMATION THEOREMS Active information tracks the m between a baseline blind search, which we call the null search, and a search that does better at the target, which we call easy to define m;lthenlatlcally, captures a profound truth. We can the alternative search. Consider therefore a search for a T in a search space Q (assume for tollOVVlnlg e:il:arnpJe. Consider an extremely large space n that we must slnlpllClty that Q is finite). The search without any knowledge target T. In other this is a classic nel~me-lll-tJt1e- about the space that could T. Bernoulli's insufficient pn)ba,blIJty of T with respect to the search is therefore extremely reason therefore and we are in our to assume the probability dis- Q as all the on Earth and T as a treasure chest buried tribution on Q is with toP =: where 1*1 is the cardinality consider an alternative search S for T conducted in the subspace of *.50 We assume thatp is so small that a or null search over Q for T (i.e., a search for T T c Q' c for which the of successfully searching for T within uniform random is to succeed. Success that in assume to be much Q' as some small place ofa blind an alternative search 5 be that succeeds with a probability Bora on which the treasure T is In this case, In =: q that is considerably larger than p. that the conditional probability Whereas p gauges the inherent of the target T via a search, q definition since T is contained in Q 1, is gauges the difficulty of locating T via the alternative search S. The question then naturally Ilkl"wilse. because Tis contained in Q', =: q.) arises how the or null search that locates T with gave way to the alternative The search has now become much easier, from all the on Earth to Bora search 5 locates T with q. In instance, starrs with a Bora. But what the search to become easier? the endogenous and exog- blind search whose in one query is 1 in 1040. This is p. He then enous it is not to know that impl"meil1ts an alternative search evolutionary algorithm) whose success m the null search has the very level In =: -log(P), but that choosing an appro- a few dozen queries is dose to 1. This is q. subspace we switch to an alternative search 5 whose difficulty level Is = -log(q) is much Dawkins leaves the discussion hanging, as furnished an algo- lower. The that needs to be is how we knew to switch search for T rithm that locates the target phrase with probability (which we are calling he has from Q to the Q'. In other how we know that ofall places on Earth where demonstrated the power ofDarwinian processes. But in fact all he has done is the prob- the treasure be we needed to look on Bora Bora? lem elsewhere, for as we in this the function Within the larger space the has =: piq follows he used for his algorithm had to be carefully chosen and constituted 1 of 1 (i.e., from T c Q' c =: p, and So the associated with this p) such fitness in furnishing an search whose probability subspace is =: log(qlp) =: when an alternative search per- success is q, he incurred a costp offinding the function, which coincides search reducing the search space, that lmpf()ved perf,orrnaJ:1ce (not coincidentally) with the improbability the null search finding the target. The must be for the active information with which recluctlon mlufJma.t1Cln problem that purported to solve is therefore left completely unresolved! original space which contains the target and therefore should chosen. iHL'~~''"'' In such discussions, it to transform to measures (note that what prclmpted us to come up with Q' in the first and how did we know it contains all logarithms in the sequel are to the base We therefore define the endogenous zntorr.rtatlOn T? Active a cost to any that enables us to answer this qu.estioll. In as -log(p), which measures the inherent difficulty ofa or null search in exrlloring the The IS a case ofthe theorem. Conservation of Information Theorem Let T be a tar- coordinate is in the target, it's to any m-query search so it is get in Q. Assume that Q is finite and nonempty, and that p we take to be mathematically equivalent to a single-query search on this Cartesian In consequence, The information let Q' be SnIQle-ClU<~rv searches such as appear in theorem entail no loss another nonempty finite space, fP be a function that maps Q' to T = {y E Q' I 1 E T = fP- Define q = ITI/IQ'I Proof. Let Q = so that T= take to be . Given a null search for Tin Q', fP induces an alterna- and let Q' tive search 5 for Tin Q. The exogenous information is therefore Is define ... ,yL, ... ,yN } so that T =0 {YJ' ... ,yJ. Then p = K/M and q = LINand as the set of all functions from Q' to Q and the set of all that = MN. From the blnlOnllaJ theorem it then follows that the number offunctions in ::::: q each such ljI maps at least as many elements of T as Then map L elelneDits ofQ' T and the rernalnulg elements ofQ' into Q \ Tis equi'valently the information associated with is bounded below active information Remarks. To see that this th<~on~m includes the as a case, let Q' be a subset ofQ and let qJ be the function that takes each element in the subset to From this it III turn the number in map L or more eleme:nts of the superset. Q' into T and the rernainirlg eJlerrlents ofQ' into Q \ Tis This theorem that the inherent ofa search never goes away. The origi- nal search on Q for T is characterized the small p of finding the target. We then that if we could conduct an easier null search on a space Q' for a target T of success q » and if there were some stI'al!shtJorward way to translate target elements of this alternative search to target elements the of the search would dissolve. But the translation ifwe divide this number the total number eleme:nts III that connects the two searches this case, the function qJ) in its own order search space (the space offunctions between the two search which includes lots ofother translation schemes. we search among them? Ac;cordJlllg to this a translation scheme that maintains the same level of pertclrnlarlCe as the function fP an at least that ofthe active information. The null search has an inherent The alternative which is a cumulative dl!;tn,buticm for a binomial random with parameters Nand p. utlJlzmg qJ, has a reduced Is = But the fP which enables It is the probability of Since the mean such a random variable is and since q = this reduced has itself no less than In-Is = I+ = log(q/p). So cOJ:lsrruc:tlDlg the alternative search does to make the original problem easier and makes matters worse. It's as one can never fool the original search. The of this and ofconservation ofinformation theorems IS that track the that was applied to augment the ofsuccess- sea.rdling for T and show that this information is bounded below the active information. In other words, these theorems show that the ease as represented Is super- can be in informational terms, at the cost of I+ =In-Is. Conservation ofinformation therefore that any in the search over a null search is not a free lunch. payment can never below the active informa- tion. In active infOrmation represents optimalpricefOr a search. a technical remark needs to be made about how we are searches. our statement of this it appears that any consists of exactly is bounded active mj-orm2ltlCIil I+ = 'V,;\'1'/ Pi. This bC;JlICldl, a search consists up to m where m is the maximum that are section the search so that its space consists the m-fold Cartesian pn)(1l1ct of search space and rede- The conservation of Illl-onmatlon theorem per'haiPS the most basic of all the the target as the set of all from this m-fold for which at least one conservation theorems. shows COllstJructmg an search that THE OF 1mlPro,ves on the average over a null one must pay for the 1mpnJv<~m,ent let denote the set all probability distributions on n and the set with an amount not below the active information. All conservation of information theorems distributions v in such that v(T) ;::>: q (i.e., each such V at least as much !-'HYUd.UHa take this one might wonder whether less ways exist search to T as j.1-each such V therefore represents a search that's at least as effective at 10c:atJ.ng pertormlan.ce, ways that circumvent conservation information. Then the uniform of which may be derlOt<~d "-.,cmS1UtT, for Steven Pinker's that the mind is a coordinated aSi;enlbJy is less than or equal to piq. Equivalently, the (higher-order) endogenous information associated com~)lltationaJ modules.51 We therefore represent the mind with finding Tin , i.e., -log(U*('I)), is bounded below the active informa an act as a search a Cartesian pnJdlJ.ct tion 1+ = -log(U(T)) + 10g(J.l(T)) = log(qlp). search spaces: which we Q. The target ~ ~ set T = x 1; x ... x 1;, each is a nonempty = ... ,xl(' X + ' •. , = Proof. Let n K 1 so that T= KIN ext:relnely small uniform in which we denote p. This is the pnJbclblillty given that J.l is a pf()b2lb1JJty distribution on it follows of a succes:stuJ search. Note that the uniform on the Cartesian pnJC111ct is the pfiodiuct of the uniform and that the uniform of T is the the uniform of the N ow as a materialist and to the where each aj is the ajS sum to 1, and each /5 is a point mass (assigning mind's success in T as some fluke that to find a needle probability 1 to the corresponding each element of has this form. It follows the The chance of the gaps is as as the of the that has the geometric structure an (N-1)-dimensional simplex consisting ofall convex gaps. he would want to attribute any such success to the coordination of computa- combinations ofN real numbers. its uniform probability is given by a tional modules where the modules and their coordination are the result a normalized Lebesgue measure. Darwinian process. Think of each of these by as wc,rkllllg Since J.l(T) = q, it follows that on its space to find a target element In other each an e1e- in T and as a result these modules induce an alternative Oi = q. 1 that delivers the the target T In this way, mod- ules basic mental functions can be seen to search n T Pinker's M(Jreov<~r, any distribution V in the modular of seem well on the road to Vllldl.ca't10n. In such an raises far more difficulties than it resolves. are these modules and are Pinker never says. But even did or could say, the that these modules are to resolve remains as unresolved as ever. To see consider that the success modules in the target satisfies delperlds on their the ofsuccess well the minuscule pnJbclb1JI1ty hi:::: q. for success ofthe null characterized a uniform U on n. Pinker's m'OG1J.les, th,~retOI'e, induce an alternative search S ofsuccess, call it q, is much bigger than p. his modules the uniform U with a new distribu- From these facts it now that the uniform prCJbclbility U* of is given the fol- tion on call it j.1, that assigns q to T expression :52 But where did this J.l come from? Did it m,lgH:aJJly materialize? it resides in the space of measures on and in that space it to be found and But how is it that we can in this space measures, a measure often called a "probability at least as ett,ect1ve as J.l at locating T? As the next theorem the (higher-order) a probability distribution v that's at least as as J.l at locating Tis less than or to plq. This last describes a cumulative beta with first parameter r = N(l- Conservation of Theorem (m.easwre-th,colretk v·er1,ion). Let T be a target p) and second parameter s = Np. substitution shows that this can be in n. Assume n is finite and Tis nonempty. Let U denote the distribution rewritten as on n ITl/lnl = we take to be The infor- mation is therefore 10. = -log(P). let J.l be a on n such that q = I( -p)- we take to that characterizes the bilistic behavior ofan alternative search S. The exogenous 1S Is -log(q). 377 cUJmullative beta distribution first pararneter r = and second param- a distribution that It is well known that the mean for this IS 53 consequence, such h induces an alternative I 11 1P"hpf··orilerJ uniform pf()ba,bilitv theorem attempts to characterize the informational nr,ronprtlPC use fitness functions target interest The that the pf()balbllity distriloU(iorlS these fitness functions are invariant under a group action is customary such theorems: it ensures that fitness is q target. As Culberson puts follows is bounded active inl~ofjmation 1+ == touted as 'no This means that expect EAs to pelrtorm wlth()llt proves the theorem. D inl'ormaLticlll from the environment. Similar claims are often made for +A.~""M·P not effective at the T and Conservation of inj'ormalticlll of mathematical known as information from environment thus NFL no free eVio!t:lti()il,lry search as 'rc.~"nn account for the difference. rUll1ctiOllS as a with each in(;!udes a free lunch result as well as a conservation lnj~OfjmatlOn result adVall1tall:le for the environment. A states that the average perrolrnlarlce the no lunch The formula ofan eVlolllti()n,uy search across fitness rW1CtiorlS blind search. Conservation of inj~orm,lti()lls connection to NFL into what functions to induce altenlative (e,'oliutlOnar1/) si~archl~S that are so much better than that across fitness functions does no bet- ter than blind mJrorm,lt1(on, active information is re(luired expresses classic im;tallce av(~ra!~ed across to locate the that ev(olutionaJry search effective. fitness tUll1ctior:IS, it shows ur:lde:rs(;ores the connection between conservation of mj~ormaLticlll the two are id,cnl:iC:ll). pnob,lbiilltY distribu- indluces a Xb ... ,Xj(, XJ(+l, ... , so that T== X2, ..• , KIN gellera!il~Y assume that N is divisible K so that K x L =N for some L. j-"X11~ !!1l1 Q with finite elements so that Thas and K does divide N set of elements OJ, ... , 0[ in the such that 1; pal~tition Q with 1; == T. include T, and their indllces a pro!bability distribution union all ofQ. Assume that each such the rollovvinLI:l Because the pf()ba bility distributions induced the fitness rUllctlorlS lilvananr An NFL result then tolJlow's: under the it follows that for any (J'in ==u Assume next we take to Bur since as throu~~h all the fitness rurlCtions and int,ornl1ation is !, == -lU'>' ",,,. fitness furlctions is closed under cOlnposition Let each such h induces it follows THE NATURE from one to another in one then it must do the same in the other 'd,.LV.l~J' in place of the full group on cardinality is the factorial of lOr relevant group action would be the group on 0', whose cal:dlnalJty In consequence, all the htJue~;s-JnGluc:ed pr()b8IbJ]Jty nueasures over IS also is the factorial of !). But in the denominator com- invariant under SQ. And this in turn each i (l ::; i::; nv,orvvh,'lrrlS the numerator. It therefore represents a huge input of active information; unless these spaces are very, very this ratio will be much less than In a similar one want to constrain the fitness functions. one think that fitness to vary with some metric structure on the search space. But where such a metric structure come from? how much does it reduce the full is constant. But since the pal·tltlOn 0 with ~ == T, it that space offitness Ifit reduced some smaller space offqtness functions , then 15'1/151 represents a addition ofactive as does the metric structure on the undel"lYlng search space 0 many other metric or topological structures were possible and what led to this one rather than the ~.,,~•.")) Christian and Marc Toussaint for that NFL theorems are unre- alistic because focus on fitness functions closed under They suggest that in and the,retore realistic problems the focus instead be on classes functions that are not closed under 55 All such and imparts active information. ==p= Mon~o,'er, once such constraints on fitness or permissible permutations are fleshed out to the where we can calculate how much active information was imparted, we find that conservation ofinformation is nrf' 7. THE LAW OF CONSERVATION OF INFORMATION have to greater But we estabJJSnled that it is to p. Fronu this contradiction it follows that ==111/151 is indeed less than or equal to plq Laws ofscience are SUjJp'Jse:d to be scope, hold with find and therefore that -10g(I11/15D is bounded by the active infornuation 1+ == log(qlp). support from a wide array facts and observations. We that conservation of informa- This proves theorenu. 0 tion is such a law. It may be as follows: This fitness-theoretic conservation of is nuore significant than it The Law ofConservation ofInformation search that raIses at first appear. One nuight that its applicability is linuited because it was fornuu- the of a target with respect to blind search requires in its for lated in such general and seenuingly unrealistic ternus. What search space, instance, allows mation an amount ofinformation not less than the active information I. = log(qlp). for all possible pernuutations? Most don't. insofar as don't, it's because structures that constrain the pernuutations. Such however, bespeak the In short, raise the search a factor ofq1p, incur an cost ad,1ltJlOn of active infornuation. Consider, for instance, most evolutionary algorithnus are The rest ofthis section consists ofbold-titled devoted to elucidating this used to search, not,a ~o~pl.etely ~nstructured space but an Cartesian product space , each 0 slgmfymg a smgle query in an m-query search. General as AVllV"VO. A null search B, which is In that case, permissible must not sCi"anab.le (l1lf':rV-()T(1Pf or vary fronu one sets a T. Think factor to the next but must act sanue way on 0' across (ifa permutation moves random variable that induces a unltorm pn)b8lbl1Jty dl~;tn.butioln on O. Regardless 380 know or don't know about T, we can B and therefore do at least as good as B of to a geller'ally Sllp(~fl()r optimizer without pf(JbJem-SjleClhc information se8lrcJlin:g n for T. The is how much can we do than B. In pr;;lctice, about a search. ofBT is so small that B stands reasonable chance Work on NFL the~or,ems, III toc:USI,ng on average pel'JOl'm;lnc:e to an alternative search 5 whose q of T is sig;nihcantly a natural what are the inJ:orm;ui()n:al p. But where did 5 come from? 5 not materialize. alg;Otllthms that in are better others? NFL is a into existence some process. LCI states that the an is counterintuitive because we know that some search alg;Ofllthims investment ofinformation not less than 1+ = at specific tasks. The Law of Conservation of as we it presupposes the NFL theorems and then the costs that make some algorithms bet- Theorems. LCI receives support from conservation th(~OrerrIS ter than others at tasks. to an the last section. Such that the to Impf(We al~~orlttlm at a specific is purchased at the cost of active information. so that its increases a of q/P is put, NFL says there is a cost for effective LCI calculates the cost. at least 1+ = log(q/p). Even so, LCI is not theorem. It says that in any circumstance where a search way to an alternative at 1+ Ltm.l~C.llI-llIUltng A.llalogue. The Law of Conservation of in both scope and the alternative search. But the forms which null and alternative th(~oret1cal computer science.61 Church- se8lrcJles can be instantiated is so varied that no mathematical theorem can about the nature of LCI as the functions in the we offered three sU[Jst;mtlaJJly dltte:rerlt types conser- a that is informally com- vatlon intonmatio,n theorems. Instead one mathematical theorem, UlC:-D;ase:UJ, it can be coded as an algorithm rUJlning for any situation in which a blind way to an an alternative search that does better than impf()ve~d alternative theorem exists that the alternative alternative was at an cost no less than The reCIUl!red at least 1+ to be instead of LCI a theorem, it characterizes task theorist in that case is to "follow the information trail" and show where the situations in which we may lel';itim;ltely prove a conservation information that this search outputs in a target was first (much as the task LCI therefore be viewed as a certain common tea.tul-es. ofthe computer scientist is to show how some that is computable can be eX]J1H:ltly hJrnmlate:d as an of being run on a machine). No Free It follows there is indeed can be no-strict the several theorems to Thesis or LCI. the two are to mclepen,derlt vi:;ritICatlOll. theorems showed how eV()JultlOllary s(~afl:he:s, that any operation that is informally no at targets than this has Schaffer's Law Conservation of com!Jar'ed a learner who can achieve "at least mance" to "a motion machine."58 ScJh.atter··s m,lchlln,es constitute a thermodynamic impossibility, chance constitutes an al~;oritblmic irnpos~,ibility. He eJabo.rat,ed, Prlob:lbiility Distributions vs. Prlob:lbj:li.stic Outcomes. Much of the power of LCI An essential property of the pnJbJem of inductive gelleraJlzatlon is that it admits no comes from its focus not on part1::uJlar pnJb:ablJlstlC outcomes but on pnJb2lblJIlty dii,tributio,ns. solution. An that is for certain sets ofconcepts must nec- LCI is not that certain outcomes or events do not, or cannot, HappeH. be bad for others. Ml)re,ove:r, no alg;orJith.m dominates any other. If It IS that certain types of cannot obtain "71th",,,. two learners differ in generalization there must be problems for which each of information. LCI the observation that different distrilJutiorls are IS to the other. As a consequence, every in some sphere as~;oclated with different in many instances can be pre ap!)Il<:atJion and each is in a sense, worthy Clse m;lth:enlatlGtJ characterizations em~lirical c(Jnslderatl()ils). These succ:esstul1y concluclmg a After M,ieneadly and initial work in additional search. According must NFL Yu-Chi Ho and David Pepyne a s1nlplIhe:d al)proac:h to these the be accouI'lted an NFL which he descnlbed exrlliCJttly in terms It a Not Computatio.nal Given alternative search that "princ:iple" and reJ,ltIrlg it to the work ofSchaffer. LH.hHC'" mspec:tinlg a the alternative search, it would be possible to calculate the information cost that was incurred stands no oflocating T, success in for T requires an alternative in its formation. And we would be wrong. When a IS search S that has q T, where q is But that raises the the of its representation may be irrelevant to the for its for- qw:stIon, how did we find S? S resides in a space, call it and specifi- mation. With computational of their on nl~,ner-olrQ(:r target of all searches that have at least q of idilosyncr,lSi(~s of the environment. searches whose targets vU5"I<" target T (for consistency let =Q and let Tl) = 'But how easy is it to are sequences bits in use fitness functions that gauge dis- LCI tells us that so at least 1+ = log(q/p). Moreover, once we've tance from the target fail to match up use found the alternative search S in we still have to use it to search for the original target T the in Q. This lower-order search has probability q which to the exogenous Now searches in space the uttcltmatlcm Is = fitness function gauges distance from a ,vt/v-un sequence the to locate the origina1 target T by first the sequence is inc;onllp:res:sible conlplltatiolnally, as we would expect with a random ill!!n(~r-;CJrCler search space for S and then using S to search for T requires at least 1+ + Is sequence of coin the fitness function gauges distance from a l,vt/v-uic = 10g(q/p)-log(q) = -log(P) = This that the endogenous information (i.e., inherent sequence the sequence is for mstance, difficulty) a search to locate the original target Tis at least as great as the a sequence of and thus the search associated it, will ongllul enldol'SerlOlls information. We represent this fact the inequality ref,re"en.talJOI1. The second one, contrast, will be much main evaluation a line ofcode that says "add number of bits < dittering from And yet both when identified with fitness will require the same amount of information to be located from the space where the first term denotes the lower-order endogenous information of finding T 0'-""'-'''/ 1 Q = functions (compare the theorem ofthe last 0 since and the second denotes the higher-order endogenous informa- tion offinding first for a higher-order target The Search a Search. In char,lCtenzlflg the information cost that alternative searches Given implies mathematical induction) that as we move up the LCI treats searches as spaces spaces each of whose search targets etc. within higher-order search elements is a the to a search out one class spaces etc., information associated with locating the origi- searches that with probability q or better locate to the exclusion of others (those nal target Twill never diminish and may well increase. We call this the LeI Regress and write that with less than q locate LCI says that the vU5",a, Q for a target Twith probability q ofsuccess is never more and possllCJly ::; In '" ::; In '" ::; .... than searching a higher-order search space a search search space finds T with that same !-'HJUd.UHiC mt'onuatlon needed to locate 1'(3) the information needed to locate 1(2) To see what's at stake in such a "search Imagme that you are on an with a search in the information needed to locate the T using a search in butied treasure. The that a blind search is unlIkely to ns we may ask, if an alternative search achieves a of a T the treasure. you have a treasure map that will you to it. But where that is respect to a null search, where did the information did you find the treasure Treasure maps reside in a possible treasure maps. The that enables the alternative to be come from? From a higher-order search? vast majority ofthese will not lead to the treasure. to find as the LCI a higher-order search at as much information to map among all these treasure What you need to find locate T as any lower-order from Peter to pay Paul at best maintains, and it? Conservation says that the information reqlUll'ed out the map is may even the debt now owed to Peter. from Andrew to pay never less than the information required to locate the treasure dil:ectly. Peter maintains or intensifies the debt still further. from one lender to pay From the searches are as real as the searched. Just as the exis- another does to redress a debt. does the LCI end? In fact, it may tence and formation of those must be explalllled, so too the existence and formation of impl'vinlg that the information that enables an alternative search to succeed in locating the searches that locate those must be We say that resid- present. it may end because an information source added in a space of searches, are themselves to be searched. This of the needed to locate T One suggests front-loading of information, the searches: the search, the search for that the search for the search that other direct input. Both evoke ""-'-H'5'A" etc. LCI says that as we regress up this search the search never becomes and may in fact become more difficult. We this next. LIll:rOT'V The LCI connection between the Law ofConservation of Information and the In and Inf,?rnzat,inn. The Kegn:ss. Consider our setup: A null search which is sets Devlin considers the th(~rrrlociynlanlicSlgmJhGlllC;e a pf()b2lblJl1stlC baseline p for se2lrcJ1lnlg the space Q for a target T Because p is so 385 information should be re~~af(:led a basic property of the universe, fine. To you need to find common to your circumstances but al()il!;sH:!e matter and energy interconvertible with In such a what's different. When you remember that your friend also consumed an inordinate amount of su;gg<:stJlon for a to be more }In:Cl~;e), information be an mtnrlSlC w11ereas you water, Mill's method to measure of the structure and order in parts or the related to This used in relevant to evolution. tn~qulently entropy in some sense its 62 some sense of to the inflated claims so made on behalf of Darwinian processes. We've cited section 5) Kenneth Miller's tends to oVlers1elling of where he claims that "what's needed to drive" increases in DICJiOQ1- the search for cal information is three and mutation."67 Mill's method of difference the lie to Miller's claim. It's easy to computer that feature unl.avaIlablllty of energy for useful work in an isolated non- mutation-and write equilibriUJ:n system, as measured entropy, tends to increase as time forward. seems, such simulations that solve and But because ml:onmatlon as characterized the of Conservation Information may be seJecl;IOJI1, fI=pLlcalti0l1, and mutation are common to both such as Mill's enltroov: in(;re:ased information indicates an con- ductIng a whereas in(;re;ased entropy indicates a de.:re:ased cap,lCll:y Nils J)aJTlci:Hi, computer simulations ofevolution as far back as under- the work necessary to conduct a search. stood this Maxwell's U(~IIIOn.63 which indicates the information source to decrease entropy over Conservation of Information The selection Darwin's sufficient to the evolution of liv- prove more basic than the Second of Ihennodyll1arlll(;S, The title Leo Szilard's cel- oq;aulisrm ifone starts with entities the property to retiroduce and mutate. ebrated 1929 paper on Maxwell's Demon is re,call1rl8 here: "On the Decrease At least one more theoretical principle a which would how m a the Inlrer'lferlrirlt "64 The information seJJ-r,epr'oducmg entities could rise to or:gaJ1isms with the and ev~)lutionary inl:ellige,nt. LH[eW'lse. the LCI as noted in po:ssilJilities which characterize or~~anisrrls, 68 mlteLllg,eni:e IS ul1:inlately the source of the information that Barricelli's here is correct: Miller's rqpli,cat:ioJI1, and muta- tion are "not "at least one more theoretical prmc:iple is needed." 8. ApPLYING LeI Barricelli's sul)sequent pn)pc)saJ for the theoretical JS What was his idea that or can combine to form 69 of Darwinism have been less favorable had scientists heeded new, more complex orJgaJ11SmS rep'!icltOl·S. Darwin's contemporary Stuart Mill. In sixteen years the pu!)licatic)il These the research of blCllo~;lSt 70 Darwin's Mill the first edition of his ofLogic M2Irglll!s, who wClrkimQ on this several decades. Although she describes the 1880s had gone 65 In that Mill out various methods many lilt:en:stJmg sYJmtliogeJleS;is, she hasn't shown this process constitutes a gen of induction. The one that interests us here is his method Mill this eral soJutJlOn to h;~.I~r.,,'e inf-onmation proc,lenl1. :c,'yrrlbH)ge:nesls, whether in real or in method as follows: virtual it cannot create fundamentally new ones. For or~~anisnls merge in the of the an instance in which the under occurs, and an instance in org;anJlsm IS the sum of the genes from the original two organisms-no new which it does not occur, have every circumstance in common save one, that one oocUlTirlg genes are created. Genuine is therefore reach. And yet, gerlUi11e in the the circumstance in which alone the two instances differ is the effect, is what the mcrease information over the course ofnatural or the cause, or an part ofthe cause, ofthe phenomenon. 66 exhibits. Neither Barricelli's nor Ma!l;uJ.ls·s propios~l1s won the The reason haven't is ESSerltl2111y this method says that to discover which of a set ofcircumstances is res;ponsJ,ble that like is another undirected way of pr,odillclng raw an observed difference in outcomes a in the circumstances associ- vanatJon in structures. To resolve hi,~ln,,,,,,/c information harness- with each outcome. An immediate ofthis method is that common circumstances that variation. For most that's the natural selection. cannot a diHerer1Ce in outcomes. neo-Darwinism locates the source Suppose you and a friend have been watching popcorn, and 10l1nl?;in,g on a milltaticlll), will a Darwinist." Yet with no vIt)ratmg couch. Yet your friend is now stalgg,ering hlf'"rV-"VF'(j whereas you are miwinlY IJrf'rl In a classic in 1967 showed what happens to a molecular other sources constitutes the nri rr1" rv HH~Uldlll'JlH nosponsibJe for the eV()lUflO,n of system without any cellular around it. The rel=)l1c:atlng the information to this mechanism must still be ex]plaJn1ed. Mon,mrer, molecules nucleic acid an energy source, building blocks the Law of Conservation of that information cannot be less than the mecha- nucleotide bases), and an enzyme to the process that is involved lllsm out in for and biological and turlCtion. In of the Then away it goes, more of the specific It follows that characterization of evolution as a mechanism for building up nucleotide sequences that define the initial But the result was that COIUpJeXJty from fails. For proper scientific is "hierarchi- these initial did nor stay the same; were not got which he means that "a at any particular level in the shorter and shorter until reached the minimal size compatible wirh the sequence must be "in terms ofentities one level down the hier- retaining self-copying And as got the copying process went faster. aCi:ol'dlng to "the one makes evolution such a neat So what with natural selection in a test tube: the shorter that Ofj:;al1ized com!J!exity can arise out This is also themselves faster became more numerous, while the ones were gradually elimi as un:acceptabJe: nated. This looks like evolution a test tube. But the result was that this evolution went one way: toward greater SJn1p!lCllty/ machine a sU!Jernal:ura! [sic] for it leaves of the The that identified here is ofthe evolution jJ'~"~;HC;l. You have to say like "God was allow your had better be ifit is to deserve all the attention it receives. But co:m!=l!e:x:- selfthat kind way out, you as well say "DNA was "or "Life also needs to be going somewhere. In in of increasing complexity has was " and be done with ir. 77 been in the service ofbuilding structures ofincredible sophistication and elegance. How evolution NFL and LCI? Coml=l1exity theonst Conservation information shows that Dawkins's is not as Stuart Kauffman unliersta.nds as he makes out. what Dawkins as of to in terms now confronts materialist theories ofevolu- The no-free-Iunch theorem says over all fitness landscapes, no tion as well. In Dawkins argues that structures that at search any other.... In the absence of any or can- first blush seem respect to a search become once on the fitness on average, any search procedure is the mechanism is in to revise the 78 But this as any other. But life uses and selection. These search means that a null search has way to an alternative search. prclCedures seem to be bat or has to get mlunmattc,n that enables the alternative search to be successful now needs to be itselfevolved and seems a rather The no-free-Iunch theorem into the Law of Conservation of that information is no less relief the and selection well on certain than the that the blind search. kinds of fitness yet most and hence use rec:onlblnatJO.n, prt:ce<:ling quotatr>on, which was intended as a retuta.tlon and all use mutation as a search where did these weJl-~Nrc)U!,ht with small be natural as well: THE the of the machine iil'ro]'~ing natural selection is to We to that effect in section 1. Such quotes appear across the Darwinian lit precisely nothing, for it leaves the lmfnr:ma'tw'n that natu- erature. But how do we know that evolution is or that any in it must ral selection requires to execute searches. You have to say sOlnethllllg like "the sciientirically urlas,cel;tain~lble? LJ,U"-nUJI- you are on an ancient and observe a steersman infvnnat'ion was " and if you allow un"r Ut:.ll1'll~, biological IS targets. and viability determine evo- lution's targets section 3), and evolution seems to be a terrific them. This claim cannot be sustained in the face of LCI. Dawkins here describes an evolutionary that Darwinian evolution is able to such targets, LCI the process let us say, m steps (or "pieces"), each of which is sufficiently probable that it could conclusion that Darwinian evolution is with active mJ:orm'ltllJn. reasonably by chance. But even m highly events, if occurring mclerlen.dently, Ha.ggsrroJm and ll1 of NFL- and LCI- can have a that's low. Dawkins himselfmakes this point: "When large inferences to Allen numbers of these events are stacked up in the end of the Orr and in and technical accumulation is very very indeed, improbable enough to be far beyond the reach of confusion. Orr's criticism centers on the as evolve. chance. "89 Dawkins here tacitly presupposes an evolutionary search space that consists ofan m-fold coevolves with an natural selecrion to Cartesian he notes that uniform on this space is the work wonders where otherwise it William No prcJdllct ofuniform on the individual factors-this is elementary probability theory) ~ree Orr a very low to such evolutionary events. In consequence, for natural selection to be a cumulative force, it's not enough Consider fitness functions that are as unsmooth as you l.e., ones, having lots of that the individual steps in process be probable (or only and few up high hills. are the best studied ofall fitness landscapes.) all these steps must, when consideredjointly, Now drop many separate on these and let them reelsonably prc1balble. And this just means the with zero justification, sub- evolve Each will get stuck atop a peak. You think stituted an alternative search for a null search. But whence alternative search? Darwinian then that Dembski's we don't get much that's But now change the envi- has no answer to this question. To Dawkins, "You have to say something ronment. This shifts the a fitness isn't cast in stone but like 'the alternative search or was ' and allow your- dejJel1ds on the environment it finds itself in. Each may now find it's no self that kind oflazy way out, you as well just say 'DNA was always there,' or 'Life was at the best sequence and so can evolve somewhat even if the new landscape is still rugged. , and be done with it."90 Cumulative as Dawkins it, Different will go to different sequences as live in different enVlfonme~nts. nothing to explain the source of evolution's creative contrast, shows that Now repeat this for 3.5 billion years. Will this process Will we evolution's creative in its and use ofactive mlrorm:ltiiJn. get different looking different kinds oflives? guess is yes. 85 PLAN FOR EXPERIMENTAL VE,RIFIC:A1'ION" stral~;ht:torwardmathematical settles the matter.86 It is quite true that over time. But our of LCI reCjUlreS a 2002 address to the American Scientific Francis then of tinl1e··mdelpelld,ent fitness functions. Given an m-query search ofa space it can be rep- the NIH's National Human Research Instltllte, the to resented as a search of the m-fold Cartesian . Fitness on this may "A with the ll!'t:1!1t;C;J!, theory is its lack ofa plan for well change from factor to factor. But this poses no to LCI. M;atrlenutics exr)erjlm(~ntal vlenilCatlOit1."91 We submit that the Law of .()n The Law of Conservation of Intor'm;au the m;Uflen:lal:lc;l1 sciences. On Raben Stalnaker, (C;lm:bri(ige, MA: MIT Press, 1984),85. views of its main focus be:comlCs 2. Fred Dretske, Knowled;:;e !ntorm'atZ/7n (i=arnbljdf~e, MA: MIT Press, 1981),4. 92 and export information. Monco'rer. 3. Free Will, and the Test," ComJ,Le)cit'} apart the roles of HHXUL1dJJY in the 1999: 25-34. perto,rrrlarlCe of systems. 4. G. K Chesterton, vr,tlJo,(lOX:y, in ColtectedWorks K C'hesterton, vol. 1 (San Francisco: do get it? what Evol'fllllg systems active information. "Tr'ucldinlgto the Faithful: A Sp,)ol1lful Makes Darwin Go Down," inl:ofJmation enable them to acc:orrlplish: mi:as;ur'mg active information Evolution Is True on 22, 2009 Enapllasis added. "Genetic drift" here refers to random m po'pu!atilon gene treqll(~ncies. too is nonteJeo,lo~;ic211. Darwinist philo:;ophet of David Hull ex!)/icitIy confirms this "He dismissed resources not because was an incorrect scientific eXjJlanalCiola, but because was not a proper scientific Conservation of Inlor'm;ltJ(Jn, eXIJ!al:lation at all." David Hull, Darwin and His Critics: The f(e,cep.tzor, EvoLuti'?/l by the Hatvard Un./ve:rsiltv 26. 7. See, for instance, F. H. Sandbach, The Stoics, 2nd ed. (lndianaFlOl!s: Hackett, 1989),72-75. IS achieved 8. Aristotle, ttans. W. Ross, XII.3 (1070a, in Richard McKeon, ed., The Basic Works OnIQTtl-()t-Jllte researchers use cherrlicals (New York: Random House, 874. from a chemical take for gr;lnted in!·orm;ni(Jn··interlsrve processes that isolate 9. Aristotle, trans. R. P. Hardie and II.8 (199a, 15-20), in Richard McKeon, ed., The and chemicals. These processes in realistic condi- Basic Works (New York: Random House, 250. tions. the amount smart chemists) 10. Ibid., II.8 (l99b, 25-30), 251. to the can calculated. IS for whose sequen- 11. Monad, Chance ann I vn.',ess, I'll (New York: tial arrangement ofcertain molecular bases the coded information that is the focus of 12. David Baltimore, "DNA Is a " Caltech and the Human Genome Project (2000): 93 a Shannon's of communication. In such experinl1el1ts, a target in'val:iaIJly exists available online at IdnabaIt2.htm! accessed April 23, 2007). mc;mIJrane) 94 13. Manfred Po"spe·cti:ve on Evolution, trans. Paul Oxford as information needs to be to a ball to land so infor- mation needs chemicals to render them useful in OnglJI1-()r-Jlue research. 14. Ears ;:)z8lthlnal'Y and M,lynard Smith, "The Ev.o!u.tionalry Transitions," Nature 374 measured. Insofar as it the Law Conservation 227-32. Sh()Wl,ng that the information either 15. Holmes Rolston III, Genes, Genesis and God: Values and Their in Natural and Human "".on,.u,u causes back in time or terminates in an information (Cambrid.~e: C:ambri,dge Unlver'slty Press, 1999),352. source. Insofar as this seems to be created for for closer of 16. "Give me lead soldiers and will conquer the world." The "lead soldiers" are the typefaces used where the information that was out was in put in. In This quote has been attributed to Karl Marx, William Caxton, and Franklin. In such the opponent of to Reliable references appear to be discover a free lunch. The proponent contrast, attempts to track down 17. Francisco J. "Darwin's Revolution," in Creative Evolution?!, eds. J. H. and J. W. hidden information costs and confirm that the Law of Conservation Information (Boston: and Bartlett, 4. The subsection from which this quote is taken is titled "Darwin's There is no great mystery in any of this. Nor such to without De:si~;ner. to the of life. as evolution chemical or 18. Richard Dawkins, The Blind Watchmaker: the Evidence otl~volut.ion Reveals a Universe W""JUU' ,ueJ'Xft eXipel"irrlenlta13\A,ul,,,.. , it will exhibit certain informational Are York: Narron, 1987),6. those prclPertH:S alc:he:nTY', where more comes out was put in? 19. Francis S. Collins, The A Scientist Presents .LV'UCftCC York; Free Press, Or ate accountirlg, where no more information comes out than was put in? 201. qUlestrolns constitutes a A systi:mal:ic 20. Theistic evolutionist Kenneth Miller the scientific ofdivine action as follows: "The indeterminate nature events would allow a clever subtle God to influence events in ways that are but undetectable to us. Those events could the appearance ofmutations, the activation of individual neurons in the brain, and even the of individual cells and affected the chance processes of radioactive Kenneth Darwin's God· A Scientist's vC~"'" IV' Common Ground between God and Evolution (New York: added. OF NATURE 21. Richard Dawkins, The Blind Watchmaker (New York: Norton, 1986),47-48. Each of these sites was last accessed April 6, 2009. See also Thomas D. Schneider, "Evolution of Bic)lol~iC:ll 22. For an event of probability p to occur at least once in k independent trials has probability l-(1_p)k. See Information," Nucleic Acids Research 28(14) (2000): 2794-99. (~p()Hrf'v Grimmett and David Stirzaker, Probability andRandom Processes (Oxford: Clarendon, 1982),38. If 41. These computer programs suggest limits to the power of the Darwinian selection mechanism. P is small and k ~ lip, then this probability is greater than 1/2. But if k is much than lip, this prob Mendel's Accountant visit and for MutationWorks visit htt'n:.llvc'w'w, ability will be quite small (i.e., close to 0). mutationworks.com. Both these sites were last accessed April 6, 2009. 23. Richard Dawkins, The Blind Watchmaker (New York: Norton, 1987),48. 42. The alternative is for evolution to constitute an inexact historical science: "To obtain its answets, particularly in 24. Dawkins, The Blind Watchmaker, 50. cases in which experiments are inappropriate, evolutionary biology has developed its own methodology, that ofhis- (last accessed 20, 2009). torical narratives (tentative scenarios)." from Ernst What Makes Biology Unique? Considerations on the 30 Urliv,ersitv ofGeorgia estimate that 10 singl<:-c<:llt:d ()rganisnls are every year; Au,torlO1I:1Y o/a University Press, 24-25. Emphasis in the original. of the Earth, the total number of cells that have existed may be close to 43. Kenneth R. Miller, Evolution andthe BattlefOr America's Viking, 2008), 77-78. ." Michael J. Behe, The Edge o/Evolution: The Search fOr the Limits (New York: Free Press, 44. See the Evolutionary Informatic Lab's "EV Ware: Dissection of a Digital Organism" at hn'n·,I/"'·W1N 153. accessed April 6, 2009). 27. Seth of the Universe," 7901-4. 45. For the details, see William A. Dembski, No Free Lunch: Cannot Be Purchased 28. ]. Bowie and R. Sauer, "Identifying Determinants of Folding and wi.thout ,[nt,e!liren'ce (Lanham, MD: Rowman and Littlefield, 2002), sec. 4.9. Se.qwenc:es: Tolerance to Amino Acid Substitution," o/the 86 (1989): 46. Leon Brillouin, Science 2nd ed. (New York: Academic Press, 1962),269. 2152-56.]. Bowie, J. Reidhaar-Olson, W. Lim, and Sauer, "Deciphering the 47. Peter Medawar, The Limits Oxford University Press, 1984),79. Tolerance to Amino Acid Substitution," Science 247 (1990): 1306-10. ]. Reidhaar-Olson and R. Sauer, 48. William A. Dembski and Robert J. Marks II, "The Search for a Search: Measuring the Information Cost "FunctionallyAcceptable Solutions in Two ofLambda " Proteins, Structure, of Level Search," Intelligence and Intelligent Informatics 14(5) Function, and Genetics 7 (1990): 306-10. See also Michael Behe, Support for Regarding forthcoming. William A. Dembski and Robert J. Marks II, "The Conservation of Information: Functional Classes ofProteins to be Isolated from Each Other," in Darwinism: Science or Philosophy?, M'easuring the Information Cost of Successful Search," IEEE Transactions on Man, and Cybernetics, eds. J. Buell, and G. Hearn (Dallas: Foundation for and Ethics, 60-71; and Hubert Yockey, Part A, 5(5) (2009): 1051-61. For these and additional papers on tracking the active information in intel- InfOrmation andMolecular Biology Press, 1992),246-58. ligent see the publications page at ntt:P:IlVo/WW.i,V()lnro.org. 29. Nils Aall Barricelli, "Numerical Testing ofEvolution Theories, Part I: Theoretical Introduction and Basic 49. the problem ofidentifying an appropriate fitness function for locating Dawkins's target phrase is Tests," Acta Biotheoretica 16(1-2) (1962): 69-98. in David B. ed., Evolutionary Computc,ition: much worse than sketched here. We focused on the subset fitness functions, which could The Fossil Record (Piscataway, IEEE Press, 1998), 166. have its at any of But there are many more fitness functions than those distance 30. J. L. "Computers the of Evolution," Science 55 (1967): 279-92. from a target sequence. Indeed, the total space offitness functions in the sequence Reprinted in Fogel, Evolutionary 95. space (see the fitness-theoretic version of the conservation ofinformation theorem in section 6) and, 31. Heinz R. The Dreams and the Rise (New York: sp(:akilll2:, would have to be searched. In ourselves to fitness functions based on thc dis- Simon and Schuster, 1989), 104. tance from a target sequence, we've informational cost. 32. Robert T. Pennock, "DNA in W. A. Dembski and M. Ruse, eds., From 50. Bernoulli,Ars (1713; 2006). Darwin to DNA Press, 2004), 141. Pennock's work on AVIDA is sum- For the of Bernoulli's principle of insufficient reason in the information-theoretic context, see marized in Richard Lenski, Charles Ofria, Robert T. Pennock, and Christoph Adami, "The Evolutionary William A. Dembski and Robert J. Marks II, "Bernoulli's o/Insufficient Reason and Conservation of ofComplex Features," Nature 423 (May 8, 2003): 139-44. Information in Search," available at 33. MESA, which stands for Monotonic Evolutionary Simulation is available at http://www.iscid. 51. Steven Pinker, How the Mind Works (New York: Norton, 1999),90-92. orglmesa (last accessed April 6, 52. This result is lil C of Dembski and Marks, "The Search for a Search." A proof is also 34. See accessed April 6, 2009). available online in William A. Dembski, and the No Free Lunch 35. Richard E. Lenski, and Genomic Evolution a 20,000-Generation Experiment with " (2005): htt~>: IIvvwVof.de:,igninferenc:e.c()m/.docl.lme:nts!' 20C) 5.03. Se:ard~in~:_Llfge_Spacei:. pdf. the Bacterium Escherichia coli," Plant Breeding Reviews 24 (2004): 225-65. 53. See Robert ]. Marks II, Handbook 36. Michael Behe, Darwin's Black Box: The Biochemical Challenge to Evolution (New York: Free Press, Press, 2009), 165. 37. Lenski et al., "The Evolutionary Origin ofComplex Features." 54. C. Culberson "On the of Blind Search: An Algoiritllmic View of 'No Free Lunch,''' 38. in John "From to Perplexity: Can Science Achieve a Unified Theory of EVC'lutz:onarv Comt1utation 6(2) (1998): 109-127. Complex (June 2005): 104-9. and Marc Toussaint, "On Classes of Functions for Which No Free Lunch Results Hold," 39. David Berlinski, The Deliil's Delusion: Atheism and Its Pretensions (New York: Crown Forum, 86 317-321. An earlier version ofthis paper is available online at 190. wvvw"m'lrc·,tol.lss:aint.net/puIJlic:ationsl il~el-'tol.lss:lint -01.pdf (last accessed 2009). II 40. For Adami's AVIDA, visit his Life Lab at Caltech at ntl'p: QUaD.calteC1l.el:tu. Tierra, 56. See the information bounds that come up in Vertical No Free Lunch Theorem that is lil go to For Schneider's ev, go to Dembski and Marks, "The Search for a Search." 57. David H. and William G. "No Free Lunch Theorems for Ur,tirnizati'Dn," IEEE 79. For the original, unedited passage, see Dawkins, Blind Watchmaker, 141. The words in italics substitute Transactions on Evolutionary Computation 1(1) (1997): 67-82. for words in the original. The words in italics are about natural selection and information; the words in the 58. Cullen Schaffer, "A Conservation Law fot Generalization Performance," lWiUJ.ut~L"tUrttftv that are about God and Eleventh International Conte'rOlce. 80. Olle Haggstrom, "Intelligent and the NFL Theorem," and 22 226, Kaufmann, 228. 59. Cullen Schaffer, "Conservation of Generalization: A Case tvr)"s,Crll~t (1995): available online at 81. Ibid., 220, 228. (last accessed 23, 2009). tilllpn;aS1S 82. Ronald Meester, "Simulation of Biological Evolution and the NFL Theorems," Biology andPhilosophy 24 461-72- 60. Yu-Chi Ho and David of the No Free Lunch Thleorern, 83. Ibid. COi'l!e,cen"eon Decision and Control, Orlando, FL (2001): 4409-14. 84. Our ancient sailor is, we say, a Turing Test in which he must distinguish the unme vIJ'Ul'~ll-',uu",,,,Thesis,often called Church's Thesis, see Klaus Weihrauch, Comp'uttlOZ!zty diated teleology in a ship's course due to the direct activity of an embodied teleological agent versus the mediated in a ship's course due to its having been programmed a teleological agent. Without 62. Keith Devlin, Press, 1991),2. the steersman, the sailor would be unable to the two forms of teleology. Such 63. "Maxwell's demon inhabits a divided box and operates a small door the two chambers of the Inclisitinguish.abilil:y, a,:co'rd.ing to Alan would suggest that the is as real in the one case as in box. When he sees a fast molecule toward the door from the far side, he opens the door and lets it the other. For the Test, see Alan Turing, and Intelligence," Mind 59 into his side. When he sees slow molecule toward the door from his side he lets it He 434-60. the slow molecules from his side and the fast molecules from leaving his side. Soon, the gas in his 85. H. Allen Orr, "Book Review: No Free Lunch," Boston Review (Summer 2002): available online at side is made up of fast molecules. It is hot, while the gas on the other side is made up ofslow molecules and http://bostonreview.net/BR27.3/orr.htmlaccessed 28, Compare Dembski's response it is cool. Maxwell's demon makes heat flow from the cool chamber to the hot " John R. Pierce, An to Orr, "Evolution's of (2002): available online at http://www.designinference.com/ Introduction to and Noise, 2nd rev. ed. (New York: Dover, 1980), 199. documems/2002.12.Unfettered_Resp_to_Orr.htm (last accessed 28,2009). 64. Leo Szilard, "Uber die bei intel- 86. Such an analysis was offered in section 4.10 of Dembski's No Free Lunch, a section Orr's review failed to Wesen," Le'its,chl-iftfu; A. Wheeler address. and Wc)iClech and Measurement (Princeton: Princeton Urliv,ersity Press, 87. and M,ICf(:ady, "No Free Lunch Theorems for U1Jtirnizati,on. prove an NFL theorem for 1983), 539-548. "static cost functions" (i.e., tWle-!Uc!epen,dellt fitness IUJo.Cl:IOlo.S) as well as for ··trme:-d,epi,ncierlt cost func- 65. Stuart Mill, A of Ratiocinative and Inductive, 8,1; ed. (1882; London: tions" tJrrle-,jel,endellt fitness turlctiow;). LOllgno.anls, Green, and Co., 1906). 88. Richard Dawkins, The God Delusion (London: Bantam Press, 2006), 121. 66. Ibid., 256. 89. Ibid. For instance, it's highly that any particular person will avoid death in an automobile acci 67. Miller, a 77- dent But that the number ofdrivers m is it becomes that none 68. Barricelli, "Numerical of Evolution," 170-171. added to underscore that Barricelli cites ofthese drivers will be killed. the same three eV(llutionalymechanisms as Miller: selection, reF,!lcation (or reF'ro,jw:ticm), and mutation. 90. For the unedited passage, see Dawkins, Blind Watchmaker, 141. 69. Ibid., see secs. 3-6. 91. Francis S. Collins, "Faith and the Human Genome," on Science and Christian Faith 70. See and Dorion Genomes: A ofthe ofSpecies (New York: 151. Basic Books, 2002). work on goes back now over 92. The form ofintelligent de"cribing here falls under what we have dubbed "evolutionary 71. in Michael Shermer, "The Woodstock of Evolution," Jczentz/u' A;'1ze)"zC~!n 27, 2005): avail informatics" (see htl:p:1 Jv;{ww.':V()ll1Io.orl~). able online at htt:p://V'{WW."ci;lm.. C()m/al:tic:!e.etln?id~,th.e-\7Vo,od;stock-ol-e,'ol,Lltio/)cpl:int=l:rue (last accessed 93. Claude Shannon and Warren Weaver, The Mathematical Communication (Urbana, III.: 27,2009). Eno.p11asls added. The occasion for M;ar@;ulis's remark was her award ofan honorary doctorate Unjiversity ofIllinois Press, 1949). at the World Summit on Evolution, G,daipa!~os 8-12,2005. 94. See William A. Dembski and Jonathan Wells, How to Be an Int,e!!e.ctu,1fLy Atheist (Or Not) 72. Brian Goodwin, How the ComJ'!e~:lty (New York: Scribner's, (Wilrrlinigton, DE: lSI Books, 2008), ch. 19, titled "The Medium and the IVlt'Ssage." This book criltic2LJly 35-36. analyzes ongltl-ot-l1te theories. 73. Stuart Kauffman, Im"estigatio.ns York: Oxford UnJlversity Press, 2000), 19. 74. Ibid., 18. 75. Dawkins, Blind Watchmaker, 13. 76. Ibid., 316. 77. Ibid., 141. Note that im(;lIi~;em is not committed to sUipel.·na.turalisn1. Stoic and Aristotelian phi eschewed the SUjlernal:ura! in the ID camp. 78. Richard Dawkins, '-A,mum;.; Imi~rOl'Jao!e (New York: Norton, 1996).