Volume 1, Number 1 JOURNAL of IDEAS September 1990 MEMETIC SCIENCE: I GENERAL INTRODUCTION Elan Moritz The Institute For Memetic Research P.O. Box 16327, Panama City, Florida 32406 Received April 23,1990 Abstract Memetic Science is the name of a new field that deals with the quantitativeanalysis of cultural transfer.The units of cultural transfer are entities called "memes". In a nutshell, memes are to cultural and mental constructs as genesare to biological organisms. Examplesof memesare ideas,tunes, fashions, and virtuallyany culturaland behavioral unit that getscopiedwitha certaindegreeof fidelity. It is arguedthat the under standing of memes is of similar importance and consequence as the understanding of processes involving DNA and RNA in molecular biology.Thispaperpresentsa rigorousfoundation fordiscussion ofmemes and approaches to quantifying relevantaspectsof meme genesis, inter action, mutation, growth,deathand spreadingprocesses. It is also argued inthispaper that recombinant memetics is possible incomplete analogy to recombinant DNA/ geneticengineering. Special attention is paid to memes in written modern English. KEYWORDS: meme, replicator, language, culture, copy, idea, evolution, computer, virus, knowledge, artificial intelligence, brain, mind. I. Memes and Replicators An Informal Introduction. In 1987 thebook "Engines of Creation" (EOC) by K.EricDrexler1 appeared. EOCprimarily espouses Drexler'svision of nanotechnology, a technology of human-designed molecule-sized machines, a technology based on the concept of replicators entities that generate copies of themselves. Allkinds of replicators surround us, themost rigorously (but not necessarily, fully) understood replicators being RNA and DNA molecules. Attention wasdrawn toa special kindofreplicator thatDrexler loosely termed mental-replicators. The ideasof replicators and mentalreplicators were first articulated in a systematic fashion by Richard Dawkins in hislandmark book "The Selfish Gene"2 (TSG) and later, in more technical detail, in "The Extended Phenotype"3 (TEP). In TSG Dawkins coined the word "meme" (pronounced 'meem' to rhyme with cream) to describe a unit of cultural transmission or imitation. While Dawkins and Drexlerprovided articulation and emphasis to the concepts of replicators and memes, their discussions remain at the qualitative,general descriptive level. However, in the same time frame, Lumsden and Wilson introduced their conceptof 'culturgen' in order to allowanintegrated discussion ofgeneticandcultural transfer. Theirtheory is articulated in full mathematical detail in their 1981 book "Genes, Mind, Culture" * (GMC), and in a more easily digested introductory book "Promethean Fire"5 (PF) which appeared in 1983. Culturgen theory isa very comprehensive theory that incorporates cultural transfer subject to epigeneticrules. Epigeneticrules,accordingto Lumsdenand Wilson,are the "genetically determined procedures that direct the assembly of the mind, including thescreening of stimuliby peripheral sensoryfilters, the intemuncial cellular organizing processes, and the deeper processesof directed cognition". Lumsdenand Wilsonargue that their theorypredicts that culture acts to slow the rate of genetic evolution, while joint genetic-cultural evolution leads to major change in epigenetic rules over a time as short as 1000 years. The books EOC, TSG, GMC, TEP and PF set the stage for rigorous understanding of cultural transfer in terms of tools successfully utilized bybiologists.Duringthisgeneralperiod,thecapabilitiesandcorapellingly powerful consequences of mass media started coming to the national foreground. When one considers mass media in light of these soriobiological and sociocultural tools, one comes to several realizations. One inescapable realization is that it is entirely possible that many political, economic, andsocialeventscanbe understood andpossibly controlled by an understanding of the process of spread and replication of cultural entities. Paralleling the sociobiological and sociocultural trends, develop ments and automated production of electronic storage media and com putershavecontinued at an unrelenting pace.The paceof the computer industry is placing powerfulcomputersand large cumulativedatabasesof information and knowledge at the disposal of most inhabitants of the United States and its economic and military allies. Developments of computer chips such the Intel 80860 and Motorolla 88000 promise to place supercomputer power in the hands of any middle class consumer who wants that power. And, paralleling the understanding that many culturalobjectscan spreadinan infectivemanner,wearebecomingaware of electronic entities such as 'computer viruses' that can spread between computersvia 'infected disks' and electronicnetworks.These computer viruses and similar electronic artifacts share many of the attributes of replicating cultural objects. Given Dawkins' concept of memes and Lumsden and Wilson's concept of culturgen, it is evident that more theoretical development of the two concepts is required before one can utilize them in a practical 1049-6335/90/0100-03 $3.00 © 1990 1MR Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 manner. While the culturgen approach may be an entirely valid repre sentation, a time scale of 1000 years (required by the theory) to test predictions is too long.At thesame time,memeshaveonlybeendefined as general constructs and lack a rigorous quantifiable definition. The challenge is toutilize thebestofbothapproaches ina constructive fashion thatcanbe unambiguously tested,and thenapplied.To thisend, I suggest that, at least initially, one work with the limiting case of the culturgen theory, where one dealswithgeneration, mutation, spread, and deathof purelycultural entities.Thesepurelyculturalentitieswillbecalledmemes sincetheyresemble Dawkins'memes(however, thememesin thisarticle are not necessarily identical to Dawkins' memes). Someof thegoalsof this paperare to: provide rigorous formulation of theconceptof memes, discusstheutilityofusingtheconceptof memes, and providea quantitativefoundationfor furtherwork and exploitationof theconcept of meme. Sincethistopicis relatively newand thedesirehere is to make this field accessible to a large community, the structure of presentation will proceed by statements, informal discussion and then rigorous discussion. Readers areencouraged toread thepaper first witha view to familiarizing themselves with the terminology, scope, and potentialitiesassociated withthissubjectmatter, andthentoreadthepaper againtoextractspecificusefulcomponentsforfurtherconsideration. Thus the terminologyutilized in the initial sections will tend to be informal; terms such as meme and replicator will be defined and refined in later sections of the paper. What are some examples of memes? Common examples include ideas, tunes, fashions,and virtually any cultural and behavioral unit that gets copied with a certain degree of fidelity. Photo-copied documents (Xeroxcopies)are primeexamplesin [modern culture] of embodiments of meme replication. Chain letters, prayers, slogans and jokes, are other (mass replicated)embodimentsof memes. An example of an extremely potentelectronic meme is the computer-virus. One typeof memethatgets reportedoften in the popularpress is that ofcelebrity based ormovie-based behavior pattern. Shouler6 reports that following the MGMmovie "TheHustler",whichdepicts the life of pool hustler MinnesotaFats, "The industryeffects were overwhelming,more than3000 new [pool]roomsshot up across the nation injust three years." Anotherspecificexampleof a continuingly powerful memeis hair style; notice the spread of [British]Princess Di's hairstyles. In order to avoid gettingbogged downin thesemanticsof what is 'behavior' and what is 'meme', and where there may be similaritiesand where there may be differences, this paper will focus on discussionof a particularcategory of memes,namelythatof 'idea-memes'. In whatfollows,the terms 'idea', 'concept', 'meme' and 'idea-meme' will be utilized interchangeably. As we proceed it must be recognized, though, that developing a theory of 'idea-memes' ispotentiallytreacherous. Manyopportunitiesforconfusion exist. There may be situations where shifts of frames of reference can occur, there are ample opportunities for unintentional substitutions of general cases for particular cases, which may lead to Russell type paradoxes[BertrandRussell typesof statementsabout sets of subsets that don't include themselves, and a variety of self referential statements discussed by Hofstader 7A9]. Historically, philosophers have dealt with the questions of theories of knowledge, abstract ideas, existence of 'perfect forms' and universal truths. Philosophers of all eras have concerned themselves with how conceptsarise, theirrelationship to the physical world,and mind/body or mind/matter questions. One of the uniform aspects of philosophical theories of ideas and knowledge is the question of 'truth' of ideas and concepts. Questions of truth naturally lead to questions of ethics and morality. Indeveloping thetheory of memes it is important to stressthat one isnot tryingto determinetruthof ideas.Truthand similarnotionscan enter as parameters that can be used to describe memes, their interdependencies, andtheirsurvival, spread, and 'death'; however, memes exist regardless of theirtruthcondition. Consequently, theories of memes must steerclearof general statements abouttruth, ethicsand morality. It will be asserted here that there are useful aspects to the thorough understanding of these so called mental replicators. In fact, it is quite possiblethatwholeprocesses of development of science,philosophy, and many other human cultural enterprises can be explored and perhaps predicted from a quantitative theory of genesis, interactions, growth and deathof memes.It is thisconvictionthatmotivatesone tosetout toexplore and quantify what is known about memes and their interactions. This activity of systematizing and quantifying properties of memes and interactions between memes is what I term Memetic Science. The remainderof the paper is organizedas follows: II. Replicators, Vehicles, and Memes Reintroduction. Here repli cators, memes, and associated terminology that forms the linguistic foundations,get more rigorousdefinitions. III. Roots. In this section similar concepts exploredby others will be visited briefly. While Dawkinswas the first to emphaticallyarticulate the conceptof memesand replicators, othersbeforeandafter Dawkins'TSG have come up with useful approaches that approximate and converge on the meme framework. IV. Population Dynamics and Replicator Equations. In this section, thebasicpopulation equations are introduced. The population equations are the modem version of the Voltera-Lotkapredator-preyequations for competing species in an ecological niche.This section restson contrib utions from Lotka10 , Volterra", E. Montroll12, R. May13, L. CavalliSforza14,15, Lumsden &Wilson,4"5 Schuster and Sgmund16, and Diedrich and Opper17. V. LanguageBasedMemesFundamentals.Herewe takeupthestudy of memes that are manifested in language,and in particular in Written Modem English (WME). The particular interest in WME is due to two facts. First, Modem English is becoming the mostwidely used language, especially in international communications. The second fact is that developing memetic science by investigating WME allows a truly scientific research approach based on unambiguous raw data which is accessible to any individual. An interesting historical aspecthere is that Markovstartedhis work in stochastictheoryby investigating statistical attributes of language18. Similarly, Claude Shannon was led to many Volume 1, Number 1 JOURNAL of IDEAS September 1990 insights in information and communication theory by investigating redundancy and coding ofEnglish language"; finally, Benoit Mandelbrot of fractal fame started his professional work in study of statistical distributions ofword frequencies21. An interesting observation here isthat it isestimated that there are1,500,000 species ofplants and animals that have already been described and named22, all of these names and their descriptions are memes. Given that the wealth oflanguage based memes exceeds that of the flora and fauna of the natural world one requires memetic constructs that correspond toevery hierarchical level wefind in the biological world. The beginnings ofclassification isembarked upon as is thetopicof complexity. Finally, thissection introduces the notion ofknowledge representation in memeticphase space. Apreferred ordering ispresented using word frequency ordering. One question explored here iswhethereach individual constructs hisown phasespaceorhasaninternal phase space which is different from the 'universal' phase space. The universal phase space isessentially that of the collection ofallindividual phase spaces, with 'universal frequencies' obtained from summarizing all theindividual phase spaces. VI. Memetic Spread Equations. Inthis section, the initial approaches tomemetic spread equations are laid out in the form of probabilities of interactions and thermodynamic weights. The complete construction of spread equations naturally follows, and is left for subsequent papers. II. Replicators, Vehicles and Memes Reintroduction. In TSG Dawkins first introduces the term "replicator" asabiological molecule that has "the extraordinary propertyofbeing able to make copies of itseir. Dawkins describes replicators in terms of several necessary properties. In order to consider an entity a replicator, the entity must possess attributes offecundity, fidelity and, longevity. Furthermore, tobe considered an active replicator the replicator must have some influence over it's probability ofbeing copied. Thus, a replicator isanything of which copies are made. Examples of replicators canbe DNA and RNA molecules, monomers and polymers, songs, sheets of paper that get xeroxed, chain letters, 'junk'faxes, books, records, videotapes, behavior, memes, ladies' fashions, patternson snake skins, etc. All these entities can be characterized by theattribute that they spawn copiesorareexamples ofentities that have been copied. In most cases, copying ofthese entities isperformed with special care toreduce any errors that may be introduced inthe copying process, and that the items copied exist for a duration that can allow further copies (or generations) tobe made; i.e. they normally donotcease toexistwhen a copyhasbeen made. Replicators can be categorized in a variety of ways. Dawkins suggested thecategories ofdead-end and germ-line replicators. Dead-end replicators give rise toa finite number of copies and have only finite number ofdescendant generations. Agerm-line replicator, isthe potential ancestor ofanindefinite number ofcopies. It is the germ-line replicator that isofconsiderable interest for us asthe item for further investigation. Now, in complete analogy with the biological cases, we seek adescriptive process that allows us totreat replicators ora collection ofreplicators as being 'alive' or 'dead'. To refine this point, one can make use of a formalism developed by Dyson23 to model the evolution oflife. Dyson looksat a deceptively simplemodel where 'aliveness* is related to order, and 'death' is related to disorder. What is of interest to Dyson is the transition from disorder toorder (as the crux of the origin of life). What emerges from Dyson's model is that death of a complex 'alive'entity is statistically possible, whereas the 'resurrection* ofa 'dead'entity is not possible. A further consequence of Dyson'smodel is that thenumber of distinct basic building blocks that primary replicators (in his case species) must be made of is greater than nine. What one can take from Dyson's work is that a reasonable number (several thousand) of molecular units, that areallowed mutations and mutual catalysis, can support transition from disorder toorder (life generation) and active replication which can be regarded as life. A particularchallenge is to recast this disorder -> order transitionin general terms, and apply it to memes and memetic constructs. One approach is toconsider memes expressed as ideas which utilize language (such asEnglish) and totrack the genesis, mutation, replication and spread of ideas which use one or more 'modern' languages on which we can performquantitative analysis. Forcompleteness one has to address thequestion of thecontext and embedding ofreplicators. Inother words, replicators may berather small, fragile entities (e.g. genes, DNA segments, words). What then directly assists replicators in their existence and struggle forsurvival in the arena of natural selection? In TSG and TEP Dawkins suggests that there are 'vehicles' in which replicators 'travel about'. In particular, to quote Dawkins," Avehicle isanentity inwhich replicators (genes and memes) travel about, anentity whose attributes areaffected by replicators inside it, an entity which may be seen as a compound tool of replicator propagation." Aside from individual organisms thatcanact as vehicles, Dawkins allows for" a hierarchy ofentities embedded inlarger entities", any one of which may act as a vehicle. While Dawkins concentrates onbiological organisms asvehicles, and memes/replicators housed in biological organisms such as brains and bodies, it is important for us to clearly understand that non-biological entities such asbooks, computers, optical disks, etc. are just asimportant (ifnot more so). The issues ofthe latterbeing phenotypical manifestations and biologically produced is a matter left for epistemologists for future discussion. At this point wereturn to memes as theprincipal item of interest. The concept of units of cultural transfer and inheritance has been hypothesized by many individuals. As early as 1935, one can find a reference to hereditary-like cultural entities in Zipf24. In discussing properties of language, Zipfidentifies the 'acteme' as thesmallestunitof experiential classification, and inparticular asa 'gene ofmeaning'. While Zipfs interest lay mainly in analysis of language and relationship of frequencies of word usage, their rank and their length, more recent investigators use units of cultural transfer to study and explain modifi cation ofbehavior. InWiener's seminal monograph onCybernetics25 one finds references toideas and collection ofideas asan interacting system. Bateson26ampli fies these in talking about ecologiesofideas and explicitly states that "in the ecology of ideas there is anevolutionary process". Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 There are many issues whenonestartsthediscussion ofevolution of ideas and/or cultural evolution. There are always questions of biological evolution independent of cultural evolution, cultural evolution indepen dentof biological evolution, interdependent biological andcultural evo lution and the questions of natural selection and fitness in a changing environment. In the past two decades, a numberof relevant exploratory books(in addition to TSG and TEP monographs of Dawkins) have been published in the area of cultural evolution which treat these types of questions. The primary monographs by Bonner27, Cavalli-Sforza and Feldman", Lumsden and Wilson0, and Boyd and Richerson28serve asa good foundation, andprovide useful references foradditional research into thistopic from thebiological evolutionary perspectivewhile Hull provides a modem philosophical perspective29. In the introduction, a preliminary definition of memes was givenas units of cultural transmissionor imitation. This is the original definition given byDawkins inTSG. InTEP Dawkins revised thedefinition ofmeme to be "a unit of information residing in a brain", with a subsidiary clarification that words, music, gestures etc. are to be regarded as phenotypic effects of memes which are perceived by sense organs and lead to 'meme imprinting' in otherbrains.At thispointone mustrealize that Dawkins has provided two different definitions for memes. In fact Dawkinshas tieddown memesto dependencieson biologicalentities,and in particular he reiterates Bonner's statement that "Memes are utterly dependent on genes, butgenescan exist andchange quite independently of memes".This last statement must be treated with great caution. Later, inthispaper, itwill beevident thatwhilebiological entitiesoriginally gave rise to early memes, this is no longer the case. It is important now to appreciate themagnitude of Dawkins' contributions tothearticulation and foundation of study of memes but at the same time also realizethat his contributionsformthe starting pointand leavesignificantand interesting work to be done. III.l Roots: Philosophical Beginnings. Thereare manyindividuals throughout recorded historythat specu lated about the nature of thought and knowledge.Highlights of the most prominent Western philosophical thinking in this area are discussed by Bertrand Russell30. We can find the rootsof memeticsciencedistributed, albeit unevenly, throughout history. The main recognizable periods are those of the early Greeks, the Interregnum between Plato and the Renaissance, theRenaissance, Darwinand postDarwin, theearly modem era, and present modem era during which the concepts of Dawkins, Bonner, Cavalli-Sforza, Lumsden and Wilson,Boydand Richerson, and Hull started taking shape. The recognizable contributors of the Early Greek Period include Parmenides, Anaxagoras, and Plato. Parmenides, father of logical metaphysics, identified thoughts withtheobjectof thoughts, andheldthat if words are used in some meaningful way, what the word means must somehowexist (objectively).His approachimplicitlyassumesconstancy of meaning of wordsand is known to lead to logical difficulties. Another early principal philosopher isAnaxagoras whointroduced philosophy to Athens as well as the concept that 'mind' was the principal cause of physical change. The earliest generally developed and most influential theory of knowledge is that of Plato originally presented in "Theaetetus" and subsequently in"The Republic"31. Plato advances the theory offorms or ideas [we'llcall them P-ideas]. P-ideas were argued tobethose ideas with which individuals are endowed at the time of birth. P-ideas are abstract constructs that exist in the absence of individuals, they were regardedas objective truths. Any object could then be described as possessing properties or qualities of one or more of these P-ideas or forms. For example a blank sheet of white paper would be described as possessing the form of rectangleness, whiteness, and blankness. Geometric propo sitions wereregarded asP-ideas thatexisted as trueabstract entities even in the absence ofa thinker. Associated with P-ideas are four states ofmind: imagining, belief, thinking, and intelligence. P-ideas operate or exist in the 'intelligence' state of mind. Representations of physical andabstract entities in terms of P-ideas, andvariationsofP-ideas, dominated asignificant fraction ofphilosophical thinking [much of which was concerned with issues of truth, supreme creator, morals and ethics]. Russell expressed the critical question asso ciatedwithP-ideas, andultimatelyontology, asfollows," Thereal question is: Is thereanything we can thinkof which, by the merefact thatwe can think of it, is shown to exist outside our thought?". During theInterregnum between Plato andtheRenaissance onefinds a small group attheUniversity ofParis, called theAverroists, whoduring themid Thirteenth Century held thebelief that immortality isassociated with theintellect, and thatintellectis an impersonal entitywhichcanexist in identical forms in different intellectual beings. This is probably the earliest conception of unlabeled memes (where theconcept of meme can be substituted for the concept of intellect). Another major contribution comesfrom William of Occam (originator of Occam'sRazorprinciple) whoelaboratedonwordsandconcepts, defining 'concepts'asnatural signs and 'words' as conventional signs. Oneof Occam'scontributions is his insistence that it is always possible to study logic andhuman knowledge without resorting to metaphysics or theology. Bymaintaining thisinsis tence,Occamcontributed totheemergenceof thescientificmethod. Later, NicoloMachiavelli's thesisthat "poweris for thosewho havetheskill to seizeit in a free competition" contributed to the thestream of thought leading to thetheory of natural selection. The Renaissance and post Renaissance periodsyielded a vital con tinuation of early Greek thinking. During this period the importance of thought andP-ideas continued toevolve. Descartes' cogito ergosum and hisCartesian geometry set thestageformuch ofcontemporary theoretical science. In declaring 'cogito', as the prime irreducible, he elevated the importance of the concepts of 'thought' and 'thinking' to the premier indisputable aspect of perception from which everything elsefollows, or with which every sensible perception must be explained. Of course, Descartes recognized thatallsuchthoughtsareprivate thoughts, perceived by the individual thinking them without the possibility of determining what another individual is able to know or comprehend about them. Cartesianthoughts of this naturewill be denotedby C-ideas. Volume 1, Number 1 JOURNAL of IDEAS September 1990 Descartes paved the way for John Locke and David Hume. Locke originated the strict empiricist approach based on the notion that all knowledge is derived from experience (except perhaps for mathematics andlogic). Locke asserted thatthere arenoinnate ideas, andthatall ideas derive from either sensation orperception of the operation ofourmind. Amajor philosophical insight ofLocke isthat all things that we perceive are 'particular' instances of those things, but that we have the ability to frame ideas about 'universals' (recall here that Plato and Aristotle had severe problems intheir treatments ofparticulars and universals). Among some of theother insights of Locke is that wecannot fully know physical things, wecanonlyknow word-definitions of them. This is important to memetics in that words and word-constructs are the principal entities we can deal with ina robust way. Additionally, Locke pointed out that many ofthe distinctions we claimbetween objects are not facts of nature but facts of language. With respect to 'ideas' thethemes that mind has no immediate objects but its own ideas, and that knowledge is the perception ofagreement ordisagreement of two ideas, arethemes that underly Locke's philosophy. Locke's work form the foundation for Hume's. Hume's approach to the notion ofideas can besummarized asfollows: a)impressions are the immediate sensations we are aware ofdue to external stimuli, b)ideas are faint images ofimpressions [we'll tag these H-ideas], c)we cannot know anything we have not had aprior impression of, and d) there are complex impressions which lead to complex ideas made up ofsimple ideas. With this foundation, Hume asserted three fundamental 'laws of ideas'. 1. Ideas are connected by resemblance ofideas; for example, a picture of Einstein makes us think about Einstein. 2.Ideas are connected bycontiguity inspace and time. Ifwethink ofone room ina house, wearevery likely to think about rooms adjoiningit. 3. Our mind is impelled to seek/postulate cause & effect rela tionships between ideas. When we are exposed totwo events, A and B, that are contiguous in space and/or time, we tend to postulate a cause &effect relationship between Aand B.Thisis particularly true if we observe the conjunction of A & B repeatedly. Philosophically, Hume argues that while wecannot know[perhaps,ever] that aparticularcause must haveaparticular effect, we will still tend to associate the ideas of A and B and searchfor a necessary connection. Hume has also given us the notions ofanalytic propositions (propo sitionsabout logic) and syntheticpropositions (about mattersoffact), with the assertion that the only knowable propositions are the analytic propositions. These classes of propositions and their relationship to memetic constructs are areas ofpotential interest tothe philosophers. The nextmajorstepbeforeDarwinis thatof Kant. Immanuel Kantis considered by many as theforemost thinker of hisperiod andoneof the principal philosophersofalltimes. Hismost importantwork, "TheCritique of Pure Reason", develops the argument that while none of human knowledge can transcend experience, some of this knowledge is not necessarily obtained inductively from experience. Kant calls this noninductively obtained knowledge a-priori knowledge. Thus there are multiple categorizations of knowledge. There aresynthetic and analytic propositions as well as empirical anda-priori propositions (thelines of division being different). Technically, according toRussell, ananalytic proposition is one in which the predicate is part of thesubject, while a syntheticproposition isaproposition that isnotanalytic. Finally, empirical propositions arebased onsensory perception. Kant's "Critique" works at answering the question offeasibility ofa-priori synthetic propositions. The Kantian synthesis is this: * outerworld(W) causesinner(I) sensation. * inner mental tools order I-sensation inspace andtime. * innermental toolssupply concepts withwhich we understand experience (collection of I sensations). * things in themselves (W-things) are unknowable. *inner mental tools include 12 'categories' ora-priori concepts: unity, plurality, totality reality, negation, limitation substance &accident, cause & effect, reciprocity possibility, existence, necessity. * space and time are subjective concepts that apply to all I-sensations. * W-things are not in spaceand time. * fallacies in logic arise when one tries toapply space and time discussion to a-priori concepts. Kant utilized his system toargue that there are 'ideas ofpure reason' (such asGod, Freedom and Immortality) and that while pure reason leads us toform ideas such as these, pure reason cannot prove their existence. In memetic parlance, this is equivalent tosaying that we can originate memes using our mental tools, but we cannot prove their truth or the existence of meme predicates. The Kantian synthesis, while somewhat aged, isone tokeep inmind as we later examine Edelman's theory ofconsciousness32. Additionally, while we got the notions ofa-priori, a-posteriori, and synthetic knowledge from Kant, Kant's "CritiqueofPure Reason" was asourceofgreat concern tomany. Tothisday, many oftheissues raised byKant remain unanswered Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 in a satisfactory manner leading some of this century's prominent physicists, such asSirJ.Jeans", toavoid the issue ofexistence ofa-priori knowledge. As the Kantian roots of memetics were being completed, the most significant biological roots wereemerging withtheappearance ofCharles Darwin's "Origin of the Species"34. Darwin's contributions are now regarded as thecenter piece of biological sciences namely the theory of evolution based on natural selection operating on results of random mutations. While there is still discussion as to what random mutation means and at what level (gene, organism, group,...) natural selection operates, all biologists and most scientists accept the evolutionary approach asoperationally true. Thisbiological evolutionary theory forms the backbone of the various socio-biological theories and is a natural componentof memeticscience. III.2 Roots. Cultural Evolution, Sociobiology,... Thelastsectionaddressed thegeneral foundations thatformthebasis forthelanguage andconcepts that allowed discussions of memes. In this section the more modem and direct foundations of memetic science are addressed. Thereare two typesof modemfoundations: thosethat lay the technical (quantitative basis) and those that explicitly refer to cultural entities as replicating and spreading entities. Without question, the two individuals who have originated the primary socio-cultural and sociobiological framework which contributed most significantly to memetic science, though not under the label memetic science, areE.O. Wilson of Harvard University and R. Dawkins of Oxford University. As has happened in the history of science before, Wilson's and Dawkins' ideas matured at about thesametime andbothmen published significant books inclose temporal proximity. Wilson's "Sociobiology"35appeared in 1975, while Dawkin's "The Selfish Gene"2 appeared in1976. This isreminiscent of the Darwin / Wallace intellectual priority questions. Over the next decade both individuals continued to contribute significantly to the clarification of their concepts. Dawkins followed upwith a more technical (but regrettably non-quantitative)book "The Extended Phenotype"3which appeared in1982, while Wilson and hiscollaborator, Lumsden, came out with a detailed rigorous quantitative theory ofgene-culture interaction in the book "Genes, Mind, Culture"4 in 1981 followed by a qualitative descriptive book "Promethean Fire"5 in 1983. Thequantitative tools required for memetics draw from two communities.The bio-mathematical roots tracetoVolterra" and Lotka10. Lotka wrote a very readable book, "Elements of Mathematical Biology"10, in 1924. Although most of the book deals with a unified mathematical description ofbiology, (starting with astatistical basis, and delving into questions of the kinetics ofevolving systems, biochemical basis, inter species rivalries and equilibrium processes, and discussions of con sciousness), Lotka isaware of thesignificance ofcultural interactions. In fact he has a 'pseudo-memetic' outlook as can be gleaned from the following paragraph in hisbook, "In the human species the communication of information from onetoanother takes place chiefly through speech, tradition and carved, written or printed records. In a recent number of Nature there appeared Professor Bohr'saddress onthestructure of theatom,deliveredon theoccasionof theawardto him of the Nobel prizefor1922. Inthishistorical survey ofthedevelopment ofhistheory hementions nearly fifty names ofinvestigatorswho directly orindirectlycontributed tothispartofour-world picture. A person intelligently reading this lecture, making the picture part of hisown mental stock-in-trade, is thus virtually endowed with fifty pairs of eyesandhands, and has the benefit of fifty brains, for the most part brains of the first rank Faraday, Maxwell, ..., Lorentz,Plank,Einstein, to mentiononlya few.It is this thought-transmitting propensity of the human species, more than any other, that gives it a superlative lead overall the othercreatures of theglobe Evolution in thiscase proceeds not merely by theslow process of selection, but is immensely hastened bythe cumulative and continuous growth ofa body of knowledge exempt from thoselawsofmortality which seta term to the life of an individual Our Galileos, our Newtons, our Thomsons, have not been singled out by a process of lethal selection from others less fit to survive. The process by which viable, pragmatically competent systems of thought (orworlddescription) areevolved is quite other than this....The decisive factor was the simplicity .... eased further advance of knowledge." The bio-statistical tools for memetics are the same as those of population genetics, namely the classical worksofFisher36, Wright3, and Haldane38. Thesetools, articulated in theearly1930's,havein factformed the basis of much of contemporary human population genetics (an excellent, readable reference onthistopicisCavalli-Sforza andBodmer's book "The Genetics ofHuman Populations"l4 which contains sufficient yet not stifling quantitative discussions). Atabout the same time (1935), Zipf published a thorough investigation ofcertain statistical aspects of language in abook titled "The Psycho-Biology of Language"24 (hence to be designated PBL). PBL is a rather remarkable product that has been largely ignored, we will use many ofthe empirical findings recorded there for the initial construction of word-oriented memetic theories. During the late 1940's we see a number ofareas emerging. Hebb developedatheory ofadaptive reinforcement39which has found much use in modeling artificial neural systems. Wiener articulated thebasics of control and communications system theory in his book "Cybernetics"25, published in 1948, and Shannon and Weaver40 laid the definitive foun dation of Information Theory in 1948. It is interesting to note here that Wiener also recognized the contribution of the British empiricists Locke and Hume. Wiener addresses the theory that mind is made of entities known as 'ideas' and that ideas unite themselves into 'bundles'. Wiener recalls thecontiguity principleofHume which allowsoneH-idea totrigger its associated idea bundle. Wiener also discusses Pavlov's experiments with dogsand theexperimental confirmationofunionbycontiguity,which Volume 1, Number 1 JOURNAL of IDEAS September 1990 inthecaseofdogs isevident intheirpatternofbehavior. Wienerrecognizes theinterest of researchersofpsychologyandsociology incybernetics, but explicitly states hisview that these communities lackadequate conceptual frameworks, and in particular, they lack tools equivalent to those of dynamics theory in physics. Zipfappears again at thistime (1949) with hislittle understood "Human Behavior andthePrinciple ofLeast Effort"41 inwhich thephysics' principle of leastaction isdiscussed. Onecanderive from theprinciple of least action much of theneeded dynamics. Unfor tunately, thefield ofpsychologywasnotready inthe1940'sforaninjection of theoretical physics. Zipfs expertise and background in philology did little to endear him or his theories to either psychologists, sociologists, biologists or physicists with significant lossof opportunities. Before passing to a detailed discussion of the direct technical foundations of memetics, it is worth mentioning the perspective of Sir James Jeans, a prominent physicist and astronomer. Jeans' views are representative ofphysicists of theGolden Age of Physics during which a new world view emerged, namely the theory of relativity andquantum mechanics. Jeans discussed the conceptual evolution ofphysics inhisvery readable book "Physics and Philosophy"33. Many physicists, who one would normally think ofasdealing with inanimate objects ofnature (such asatoms, electrons, starsand galaxies), found themselves concerned with the interaction of observer and observed entities. Concerning the importance ofthe entities wecall ideas Jeans says: "What were mere associations of ideas in the brains of animals readily became translated into natural laws in the mind ofthinking men Butnowthecomplication intervenes that our minds do not take kindly to knowledge expressed in abstract mathematical form. Our mental faculties have come to us, through a long line of ancestry, from fishes and apes. At each stage the primaryconcernof our ancestorswas not to understand theultimate processes of physics, buttosurvive in the struggle for existence, to kill other animals without themselves being killed. They did not do this by pondering over mathematical formulae, butbyadapting themselves tothehard facts of nature andtheconcrete problems ofeveryday life. Those whocould not do thisdisappeared, while thosewho couldsurvived, and have transmitted minds to us which are more suited to deal with concrete facts than with abstract concepts, with particulars rather than universals; minds that are more at home in thinking of material objects, rest and motion, pushes, pulls and impacts, than in tryingto digestsymbols and formulae." However, all this is totrick us. The fact that ourbrains areorganized todeal with concrete facts does not force nature to actually be made up ofsimple entities digestible toourbrains. The physicists of the Golden Agediscovered, to theirchagrin, that forcessuchas Newtonian forces do not have real objective existence, they are instead "mental constructs which we make for ourselves inaneffort tounderstand the workings of nature". Quantum mechanics led to the realization that one cannot describe physical processes in terms of theusual concepts of time and space. The trend of our understanding of nature is consistent with Einstein's view that,asJeansstatesit, "asexperimentalresearchadvances,the fundamental lawsof nature become simplified more andmore, and, as in many other departments of physics, we find this simplicity residing neither in the physical facts, nor in theirexplicit pictorial representation, but solely in the mathematical formulae that describe the pattern of events." There are other notable discussions in Jeans' bookconcerning the different interpretations ofspace andtime. Thediscussion ofconceptual spaceand time is particularly interesting becauseit showsthat the notion of memes is immanent. Jeans provides the following description of conceptual space, "Conceptual space is primarily the space of abstract geometry. It has no existenceof any kindexcept in the mindof the man whois creating it by thinking of it, andhe maymake it Euclidean or non-Euclidean, three-dimensional or multidimen sional as he pleases. It goes out of existence when the creator stops thinking about itunlessof course he perpetuates it in a text-book." Jeansisofcourse incomplete inthat heignores the fact that conceptual spacecan exist in somerespects in memory and can be recalled by the original thinker of theparticular conceptual space. However, weseesome of the basic features of memes inbisdescription. For Jeans, conceptual space can exist in twoways,one in the mindof a thinker,and theother in a textbook. Already, by theactof transcribing a thought, one iscreating a representational replica oftheconceptual-space-thought inthetextbook. Next, when onereads thetextbook, onecreates another representational replica of the conceptual space in the readers' neural system (i.e. the reader's brain). Obviously there is no way to ascertain that the original conceptual-space thought is replicated identicallyinthebrain of thereader, however, the fact that we all can conceive of some things, write instructions down forcreating them, and then have others produce that which wehave described, indicates that certain degree of replication of thought is possible. Again precise discussions require an elaborate mathematical representation; thiswillbe provided later. Wenow come to thecontemporary foundations of memetics. There have been a number of individuals who have contributed directly or indirectly. While the theories of Dawkins and Wilson and Lumsden deserve special attention, there are a number of other individuals that have contributed. All those individuals who have concerned themselves with cultural transmission have contributed in a broad sense. Cavalli-Sforza and Bodmer42, havediscussed culturalevolution and itseffecton natural selection as earlyas 1971. They recognize the important fact thatrate of cultural evolution ismuch faster than biological evolution. They charac terizecultural evolution in termsof invention and infective transmission, and state their perception that "the interactions between cultural and geneticevolution have notbeeninvestigated inanydepth". It isclearfrom theirdiscussion thatitwould bea longtimebefore a scienceof memetics would be ready to emerge. (My informal observation here is that while the kernel of cultural evolution was articulated, and the bio-mathematical tools readily available, the focus was on relating cultural entities to genetics. While this aim is admirable, it is a severe constraint due to the Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 fact that no useful planned experiments can take place over a human lifetime. The only type of discussion that can take place is analysis of historical data toopoorlydocumentedto yieldmorethanbroadqualitative statements.) Clearly, the major text to present a coherent, well formulated theoretical and semi-empirical basis for cultural evolution is Wilson's "Sociobiology"24. There have been many discussions of thispivotal text, withall kindsofaxes togrind by differentcamps.Again,what is important to stress here is that memetic science, at this point, should not strive to generatea broaddiscussion ofbiological orsodobiologicalprinciplesand goals.Memetics shouldaim to explainthe mechanism by whichcultural entities, and in particular language and word based replicators replicate! Thus as one discusses "Sociobiology", one must note its excellent and logical presentation of thebasic mechanisms of population biology,group selection,time-energybudgets,communication,andofcourse,discussion of particular social species.However, this treatise still does not address culturalreplicatorsas replicatorsand objects requiringspecificstudy. The stage is set, however, for Dawkins. In 1976 Dawkins' TSG appears. Dawkins, in TSG mentionsSir Karl Popper's analogy between scientific progress and genetic evolution 43. Dawkins also refers to L. L. Cavalli-Sforza42, F.T. Cloak44, and J. M. Cullen45, in hisdiscussions of memes,and toE.O.Wilson's tome, "Sociobiology", as a general reference. As mentioned earlier Lumsden and Wilson introduced their concept of 'culturgen' shortly after Dawkins articulated the concept of memes. The culturgen concept makes its first appearance in the July 1980 issue ofthe Proceedings ofthe National Academy ofScience (USA) *6. L&W loosely defineculturgen as an array of behaviors and artifacts that are transmitted by a cultural speciesduringthe process of socialization. The roots of the word culturgen, from Latin, are cultur (culture) + gen (produce). Cultergens aresubsequently used fortheintegrated discussion of genetic and cultural transfer. Theculturgen theory is developed and refined inseveral articles4*50and two books *A. Ultimately, L&W suggest that culturgens can be equated to the "node ofsemantic memory"50 (this is in factan evolution of theoriginal culturgen, and moreclosely related to the concept of memes as they are utilized here than the original culturgen). Lumsden and Wilson provide references to a number of cultural constructs in their books and papers. The reader is referred to GMC4for these references. Closely related tothetheories ofLumsden andWilson andDawkins, are the quantitative formulations of Cavalli-Sforza and Feldman, best represented in their book "Cultural Transmission and Evolution"15 which appeared in 1981. CS&F areaware of Dawkins' memes; however, they argue thatitishard toobserve discreteunitsofimitationordiscrete changes in cultural traits. As the title of their book indicates, they focus on the mathematical theory of transmission of cultural traits. To their added credit, theyrecognize theimportance andutility ofstudying theevolution of language. In their words, "Our first topic is the evolutionof language, an issue less fraught with emotional overtones than say, social interactions and inequality, or altruism. Language also has the advantage of 10 reliable, accurate measurement not only because of the nature of theculturalobject understudybut alsobecauseof the tradition of rigor thathascharacterized thisdiscipline". The availability anddesirability of language as a domain of testing of memeticscience is thus implicitlyrecognized. While Dawkins, Lumsden and Wilson, and Cavalli-Sforza focused on cultural transmission in general with distinctapplication to humans, John Bonner of Princeton University investigated culture in animals. Interestingly enough, Bonner'sbookwas also published in thisexciting period (1980). Bonner's very readable text, "The Evolution ofCulture in Animals"27, generalizes discussion of culture; with culture in animals being theprincipal subject matter. Inthisbook Bonner takesupdiscussion of Dawkins' memes, and makes use of the word meroeas "any bit or any collectionof bits of information passedby behavioral means from one individual toanother". Bonner clearly doesnotfavor attempts at lumping genetic andcultural selection (as Lumsden andWilson have done). Bonnerstressesthreemajordifferences betweengeneticandcultural evolution. To Bonner, modesof information transfer, ratesof evolutionary change, andasymmetric dependencies ofgenes andmemes oneach other are critical differences. Wewill amplify someof hisobservations laterin this paper. A lateryetstill major contribution tothefield ofcultural evolution is the monograph by Boyd and Richerson "Culture and the Evolutionary Process"28. Boyd and Richerson restrict their attention to structures of cultural transmission in humans. In a manner reminiscent ofLumsden and Wilson, they linkmodels of cultural transmission to models of genetic evolution to yield what they call "duel inheritance theory". While their model makes useof themathematical machinery of population genetics, their stated goal is "not tomake quantitative predictions" but to" clarify thelogical relationships between cultural transmission and other Darwi nian processes.... that may eventuallyallow ustomake general statements abouttheevolution ofhuman behavior". BoydandRicherson makeapoint of definingcultureas follows, "Culture is information capable of affecting individuals' phenotypes which they acquire from other conspecifics by teaching or imitation" Heretoowesee the importance of theconcept of imitation, however B&R shyaway from specificsof thenature of the'information' they refer to. They adopt much oftheformalism and nomenclature ofCavalli-Sforza and Feldman15 aswell asgeneral reluctance todiscuss culture interms of particulate units such as memes or culturgens. B&R alsoexpress reser vations about the cultergenic "thousand year rule" and call for exper imental studies of a "laws" of cultural transmission. Finally, intherealm ofmathematical biology, oneneeds tomention Brooks' and Wiley's casting of evolutionary biology in terms of ther modynamic andentropic consideration. Brooks andWiley present their efforts toward a unified evolutionary biology theory in "Evolution as Entropy"51 where they detail calculation ofinformation theoretic entropy 10 Volume 1, Number 1 JOURNAL of IDEAS September 1990 for a number of examples of evolutionary process models. B&W's work is representative of a newbreedof evolution theoristswhoare searching for an entropybased unified theoryof evolution. While the sociobiologists and ecologists were busy developing alternativemathematical andlogical formulations ofevolutionary biology, a philosopher of biological systematicsand taxonomy was articulating a model for the development of science. David Hull, of Northwestern University, used his extensivebackground in philosophy, biology, and history of biology to detail a model for describing what he calls "an evolutionary account of the social and conceptual development of sci ence". Hull's model and extensive theory is presented in a detailed, excellently researched book"Science as a Process" 29. In thisbook, Hull reflects on Dawkins' memes, Lumsden and Wilson's culturgens, Boyd and Richerson's and Cavalli-Sforza and Feldman's theories, and a host of otherrelateddiscussions. Hullprovides a wealthof discussion of episodes inscience whereonecanobserve cooperation, competition, mutation and selection. Hull accepts Dawkins' memes and replicators as appropriate concepts but rejectsDawkins' vehicles; relative to Boyd and Richerson hestates"Onmyview,conceptual entitiesarereplicators, nottraits".What one is leftwith uponreading thisbook is thatsomeof thebasicconcepts fora science of concepts arehere,andto quote Hull again, "The fantasies of Oz must be made as familiaras Kansas. There really is no place like home". Withthesephilosophical andtheoretical rootsinplacewecanproceed to thedetaileddevelopmentof a rigorousframeworkfora scienceof ideas. IV. Population Dynamics and Replicator Equations. The thrustof thissection is to introduce somequantitative toolswith which todiscuss theamount of replication that takes place inpopulations thatcontain objects thatgetreplicated. Since thecommunity thatisbeing introduced to thememe concept is made up of individuals with varying mathematical backgrounds, thediscussions henceforth will omitrigorous mathematical proofsin favorof outlining critical points. Someof the original investigations dealing with replicating objects were concerned with describing population growth. In this case, the replicating objectsare biological organisms, and the itemsof interestare describing historical population data and predicting future populations (particularly human). The simplest situation to describe is that of unin hibited growth of a singlespeciespopulation. If we denote by N = N(t) the numberof individuals of the single species population at time t, the equation describing the rateof changeof N is dN dt ~AN (1) with A being a constant. This equation models a rate processwhere the rate of increaseof a populationis directlyproportional to the population. The solution of equation (1), as expected, is an exponential one with N(t) 11 = N0 exp(At), N0 being the initial population.A more realistic model is one where there are some inhibiting factors. The simplest rate equation that can be used to describe a populationwith an upper limit is dN 2-T-AN-BN2 dt with A, B constant. An alternate form of this equation is dN ( N\ with Ak = B. The solution of equation (2b) takes the form N 1+Cexp(-At) (2a) (2b) (3) with C being a constant of integration. When plotted, this solution yields an S shaped curve knownas the logisticcurve. The singlespecies model with finite resources was used byPearl and Reed52 tomodel the population of the UnitedStatesfrom 1790-1910.Pearland Reedobtainedaverygood fit to the then observed population data (see Lotka, reference 10). Their model resulted in the expression Mi 197,273,000 (4) l+exp(-0.0313395/') with t' being the time in years from the referencedate of April 1,1914. The graph correspondingto this logisticcurve is depicted in Figure1. PEARL-REED MODEL OF U. S. POPULATION 1706 17S8 Figure 1: Example of a Logistic Curve. The single species bounded growth model is formally identical to models that are used to describe the spread of infectious diseases (in an epidemic) and todiffusion of innovations15. u Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 The next step in developing models of replicators is to consider interacting replicators. The simplest multi-species environment is obviouslythe two species predator-preyidealizedecology. If one denotes the populationof species-1andspecies-2by N, and Nj, thesimplestmodel is a linear first order model dNt-£-aNx-bN2 dN2-^^cNt-dN2 (5a) (5b) wherea, b, c, and d are positiveconstants.The pathologiesof this system of equations have been discussed by Davis53. Davis shows that if one defines A-k-a2 then thesolution of this system isexpressed by: M =A cos(VA/ +p) (6a) N2=Bcos{VKt+q) (6b) where A, B, q, and p are determined by initial conditions (there are consistency relationships that relate parameters and populations; these are not discussed here). A quick observation here is that Nt and N2 have a sinusoidalor harmonic functional form and there is an obvious phase lag relative to each other. Additionally, one can explore the relationshipsof N, and N2 in a phase plane representation,this typeof analysis is presently popular especially for nonlinear chaotic systems. A more realistic generalization is the one studied by Volterra and Lotka. Their approach models the populations of one species that preys on a second species. The population of the prey species is Nj while the predator population is given by N2. Qualitatively what happens is when the prey population, Nt, is large, the predator species has 'easy food' and its population N2 grows.As N2 increases,N, decreasesresultingin a tight foodsupplyandstarvationfor thepredators.The reductionin N2 thenleads to increases in Nt and repetition of the entire cycle. This Volterra-Lotka processis described by the coupled nonlinear equations: dN,-jj-aN^-bN^ dN2 (7a) (7b) Adetailed mathematical discussion ofthis system isgiven inDavis59 and will not be repeated here save to say that there exists a phase relationshipbetween predator and prey populations(as in the linearcase), while the oscillations in population are not harmonic. The existence of a stablearrangementbetween the two populationsiscriticallydependenton initial conditions, and can easily result in a catastrophe for a balanced system. One can easily generalize to a larger number of interacting species with morecomplicated interactions. Schusterand Sigmund16use theform: 12 dN; I <J>\ ^-*(Wi tfJ-J) (8) to describe generic replicator equations. By definition, in their system, M + •••+M =c is a positive definite invariant and2MF; =$ is a fitness functional. While it is possibleto exploredifferentordersof replicatorequations, it appears that equations of order 3 or 4 are sufficient to capture most of the dynamical aspects of simply-interactingspecies. An example of a homogeneous replicator equation of order 4 is: ^-^2«WWi*»--J (9) where summation extends over the indices j, k, 1,and m. Note that lower order equationsmay be recovered by a suitablechoiceof the coefficient matrix and initial conditions. A critical shortcoming of these type of replicatorequations is their inability to deal with mutatingand emerging species as newly appearingspecies. Another shortcomingis the absence of explicitdiscussion of spatial relationships (for memetics'distance' is not necessarily limitedto geographical distancebut can includea gener alized distancein an appropriate phasespace). It is howeverpossible to conceive of the replicator equations as summarizing the 'population statistics' of competing traitsin culturaltransferor of competing memes. Ifone carefully examinesquantitative works exemplified by CS&F15, L&W4' andB&R28 [summarized indetail byB&R] onewould notice the prevalence of replicator type equations (especially in discussions of diffusionof innovations).Another recurrentfeatureis theanalysisin terms of cultural transmission along vertical, horizontal,and oblique channels with associatedbiasingdescribedin termsof probabilitiesof occurrence. A generalized Fokker-Plank equation is also implicitly or explicitly presented for calculating evolving probability densities in terms of individual meme frequencies4'1*28. A prevalent featureof most quantitative theoriesof culturaltransfer is the reliance on the extensive mathematical machinery developed in theoretical genetics to treat biparental transmission with cultural allele 'inheritance'. The models typically work with a dominant/recessive representation and eventually progress to multiple state representation based on rigorous but a-priori probabilistic formulation. While these canonical approachesare suitable for addressing the standard questions of genetic analysis and ethnographic descriptions, they do not lend themselvestodirect extensionsfor answeringthe core questionsthat face memetics, and ultimately the micro-theory of cultural evolution. In particular, as expressedby B&R, these theories ignore the detailed nature of the informationthat is passed,and the way that detailed natureaffects the phenotype. This state of affairs has led B&R to remark that "our understanding of the neurophysiology of social learningis at a primitive state". Finally, to summarize the state of affairs regarding quantitative theories of cultural evolution it is useful to quote B&R, who in their concluding observations about the fieldstate [ref.28, p 299] 12 Volume 1, Number 1 JOURNAL of IDEAS September 1990 "Wehave takenas our task the constructionof simplemodelsfor as many of the basic mechanisms of cultural evolution as we could find suitable detailed suggestions for and for which we could make a plausible empirical case. ... Like a sixteenthcentury map of the world, the scale is small, distortions undoubtedly exist, some of the processes includedare likely to prove apocryphal, and large areas are blank.... much hard work remains to be done." V. Language Based Memes. The development of a generalized quantitative theory of cultural evolution is probably one of the more ambitious pursuits of modem science. In the remainder of thepaper wewill address only a part of this goal,namely thedevelopment of a rigorous science of ideas. Thisscience ofideas hasasitsultimate goal theelucidation ofthemicro-dynamics that govern theinitiation, combination, mutation, spread anddeath of ideas. Tothis end, direct discussion of theinteraction ofphenotypic expressions with genotype manifestations is omitted. Rather, a fuller discussion of some particular language based and information/knowledge based mechanisms is pursued. A useful basis and context for language based memes is that of knowledge representation. Moritz54 argues that Homo sapiens' premier role in nature isdueto theextremely highly developed human abilities of information manipulation, knowledge extraction, and knowledge appli cation. Since the invention of language, continuing through the intro duction of writing and record keeping, and culminating in the unprecedented pace of development of computer software andhardware of thepast five decades, progressively more powerful tools have been developedthat aidand amplify human cognitive abilities. The kernel of cognitive abilities and cognitive function amplifiers iscomposed ofthree principal components: 1)knowledge, 2) physical structure, and 3)[inter and intra system] communication channels and protocols. Withrespecttocommunication channels, transmission of cultureand spread of scientific researchare two activities that could notexist without the tools language provides. Infact, language acts asthe principal element inall vectors (e.g. speeches, books, journals, TV, radio) that spread culture and ideas. A key todevelopment ofthetheory isthe realization that language is a particular manifestation ofa communication strategy. Furthermore, the communication strategy isgoverned by thermodynamical physical prin ciples, where the relevant thermodynamic representations are best expressed interms of information theoretic and complexity measures. Processes that involve ideas or memes are dynamic processes of information and knowledge manipulation. Any process of this nature is referred toasa Knowledge Information Process or KIP. Examples of KIPs in machinebased systems include:communications of ASCII files via modems, representation of information in a semantic net, query processes in a relational database, merging of two dissimilar databases, extraction of rules from data for expert system construction, application ofknowledge-based system heuristic rules, training ofanartificial neural 13 networkclassifier,extractionof a featurevector fromrawdata,generation of logical inferences or hypotheses in knowledge based systems, and, in general, execution of any data processing algorithm. KIPs have been present in biological systems much earlier than in machines. KIPs in [mammalian] biological systems are processes that engage the brain and/or the central nervous system (CNS). Examplesof [human] neuro-biological KIPs include: seeing and enjoyinga painting, giving a lecture on a technical subject, performing a mathematical calculation, writing a letter to a friend, and numerous other high level cognitive activities. Other neuro-biological KIPs involve non [directly] observable low level processes such as biological memory formation, synaptic transmission, flowof information from thecortex to theamyg dala, and interand intraneuronal processes. With the definition of a KIP Agent as any biological or machine Knowledge/Information Processing entity (e.g., child, adult -human, computer, fax machine), it is possible to explore knowledge formation, knowledge representation and knowledge spread as activitiesthatoccur withinand between KIPAgents. UseofthenotionsofKIPsandKIPAgents will allow application of memetics to knowledge/information processes in both biological and machine systems. In this context werecall that there area number ofdistinctly different categories of memes. In particular one can distinguish: 1) linguistic memes, 2)visual memes, 3)musical memes, and4)procedural/behavioral memes. These categoriesarenotorthogonal; infact,there maybeelements common to two or more. Linguistic memes are those weare familiar with through language interactions. Visual memes are those that are integrally connected with twoor three dimensional visual representations (these may bepatterns on moths andbutterflies, designs on American Indian tapestry, international road sign symbols). Visual memes depend on and evoke activity inthe 'visual* senses. Similarly, musical memes are dependent onthe auditory senses and cannot be described faithfully viaeither language memes or visual memes (e.g. bird and whale songs, symphonies, popular tunes). While one can utilize linguistic memes to describe the procedure with which to generate visual or musical memes, the linguistic procedure description will be entirely different from saytheMona Lisa or Beetho ven's Fifth Symphony. The information measures useful for our discussion come from rigorous information theory55, and include measures such as selfinforK mation Ik =-log^fo) and entropy H - - £ PfaJlqgzPfa) (where ak is the k-th letter of the alphabet ofKletters, and P(a,J is the probability ofoccurrenceofthe k-th letter)arequantities that describe unexpectedness in information, not meaning. Measures that describe value ormeaning of stringsof lettersaredistinet frominformation-theoreticmeasuresandmust betreated extremely carefully. Brillouin55distinctly associates value with possible use by a livingentity. Ultimately, we willaddressvalue in our discussions. [A temporary hypothesishereis thatvalueis relatedtoentities further up on the hierarchy of units (not words or lemmas,but certain collectionsof them)]. 13 Volume 1, Number 1 Moritz: Memetic Science: I • General Introduction September 1990 Language is a very broad topic; when reference is made here to language we restrictour attention to the written manifestation of a very specific language, namely written modem English. This is not a severe handicapsincewhatis developed hereappliesbroadlytoanyotherwritten language(of any age). A valid argument may be made that one needs to alsoconsiderspokenlanguage. Detailedconsiderationofspokenlanguage is left for another time. However, one should notice the clear benefit of using written language, namely the vast amount of real, objective, empiricaldata available in the form of publishedmaterialof all kinds. An interesting by-product of this investigation is the potential applicabilityof languageevolution rules, and replicatordynamicsin the area of computer systems. Computer languages are after all, highly stylized languages with very deterministic components. Furthermore, certain collections of computer instructions exist which fall into the replicator category (re-usable code can be seen to be a type of passive replicator,likewisecomputervirusesare a typeof active replicators). The emerging fields of computer simulations using genetic algorithms, self programming, true-artificial intelligence and machine intelligence belong to the class of areas that are derivatives of memetic science. V.l The Core Program of Memetics. Initially thecoreprogram ofmemetics is todemonstrate that: 1)ideas (memes) develop according to certain predictable rules, 2) culture transmission andspreadofideasofalltypes(inparticular, scientificideas) embody these rules 3) there is a distinct similarity ofevolution ofmeme building blocks tothai ofgenetic buildingblocks (which raises theobvious question of whether language structure is controlled by human genetic structure), and4) new, unanticipated language andmemestructures can, andpossibly already do, exist. The question may arise astothejustification for working with written language. Many approaches are possible for investigation of replicator dynamics in language, and language evolution. One reason described in theintroduction wastheaccessibility ofrobust experimental data. Another prime reason is that written language embodies a significant degree of precision. It is crucial to state, and re-state, that the most accessible memes available forknowledge representation arelinguistic memes(i.elinguistic informational replicators) or L-memes. L-memes have syntactical, grammatical and semantical attributes. The most successful general implementation ofL-memesisthrough the use ofWritten Modem English orWME. Studies oflanguage useinscientific publication hasconclusively shown thatWME is"byfartheprimary languageof international research" (Garfield57). Similarly, spoken English isthe principal language for verbal communication between individualsof differing origins, (e.g. English is theprincipal language for communicationbetween international air-traffic controllers andpilots). It isclearthatresearch publications constitute one of the major, if not principal, forms of knowledge documentation. It is thus quite probable that WME is the principal form of knowledge representation. However, WME is not necessarily the most efficient or machine accessible form forknowledge representation andmanipulation. 14 Before proceeding, one needs to view the place of written language in the hierarchy of communication strategies. Communication strategies for humans may embody any one or more of the physical senses. The most practical, in terms of their range (both distance and frequency spectrum) are those based on optical and acoustical strategies. Among the optical and acoustical communication strategiesone can observe the following general classes: i)genera] soundwithwhichit isverydifficulttoassociateprecise meaning (additionally, a limitedvarietyof differentiable soundscanexist here). ii) stylized sound such as music. Here again, it is difficult to associate precise meaning, but distinct differences are possible. In fact an infinity of variations are possible; many parameters are available to work with [frequency, amplitude, duration, modulation, simultaneous superposition of individual patterns,...] iii) verbal or spoken language. It is easy to associate meaning in communication usingspoken language, butof ambiguity is still present. It is normally subject toonesability of recall. Spoken language cannot be re-examined (thishas improved thiscentury withtheavailability of tape recorders, which makes re-examination of speech possible for the first time). Inverbal language, there exists an infinity of sequential assembly choices of finite extent[limited by number of wordsin a seriesthatcan beperceived asa unit and can belogically analyzed]. Verbal communi cation isnot dependent onsensory apparatus tothe extent that it iswithin certain amplitudeand frequencyranges. iv)written language. Written language is primarily a visual communica tion strategy, although it is usually initially based on the learning of a verbal communication strategy. Here, there exist an infinity of possibilities. Written language isavailable for re-examination leading to reduction in ambiguity, and requires less ability for precise recall. This last feature is crucial since more people can make use of complicated information relative to verbal communication. Limitations still exist since complexorlong sequencescanbeunderstood onlybyasmall setofpeople. v)symboliclanguage. Symboliclanguage isaspecializedsubsetofwritten language. Here math, physics, music (to name a very few) concepts can be described precisely and denoted by symbols. Symbolic language is a result ofconsensus formation (as to thedefinition ofsymbols). Symbolic language alsooffers an infinity of possibilities withthesame advantages aswith written language butwith more rigorous intellectual requirements onusers. Symbolic languageactstolimit thenumberofpeople with access to the full use of this communication strategy. Note here that computer languages form a special subset of symbolic language. Computer lan guagesarequite interestingbecauseofthedegreeofprecision they require. Computer languages are designed to force different machines (e.g. electroniccomputers) to execute instruction identically and repeatedly. An interesting trend in computer software andarchitecture design is the 14 Volume 1, Number 1 JOURNAL ofIDEAS September 1990 developmentof ReducedInstruction Set Computer [RISC] architectures and improved algorithms that optimize performanceover general purpose architectures. And finally, vi) visual language, as in using motion of limbs, the whole body, other body parts, or extension of body parts, tools, and flags. Visual language may includesignlanguage orinterpretive cues.Itshares manysimilarities with general soundandmusic.However it is limitedby severelimitations with respect to the numberof distinct concepts/ideas/signals expressible and receivable. Most beneficial use of visual language is in that often, gradients invisual flowsarethecuesoneuses forfight/flight information. An axiom of this paper is thatlanguage is madeup of combinations ofdiscrete elements. There are anumberofcandidate "atoms" of language. Written Modem English (WME) is obviously made upof discrete strings of letters taken out of a finite alphabet of 26 letters, roman or Arabic numerals, spaces and punctuation symbols. Spoken Modem English (SME) is recognized by linguists to be made up of a finite number of elementary sounds known asphonemes. While it is clear that spoken language appeared beforewritten language, dear correspondences exist between letter combinations and phonemes. In fact, Sejnowski and Rosenberg5^ have demonstrated an artificial neural network system, NETtalk, which can produce speech from textafter algorithmic training [NETtalk wastrained withthe1000 most common SMEwords, using 29 input nodes and 26 output units]. Another candidate building block is "molecular" innature whencompared witheither letters orphonemes. The natural molecular linguistic building block is the morpheme. Linguists define themorpheme to be the minimal unit of grammatical structure59. The important feature ofmorphemes isthat agiven morpheme usually has a dear and constant meaning in all its uses. While morphemes have a constant WME representation, a given morpheme may vary in its SME representation (i.e. it mayhavedifferent pronundation). While morphemes constitute the molecular building blocks (made up of letters which can be regarded as"atomic" units of WME), there exist other categorizations of elements of WME. It is particularly worthwhile toobserve theevolution of categorization in themajor studies of Kucera and Francis6*61. In their 1967 study, Kucera and Frands listed the relative frequency of occurrence of overonemillion words(of what isnowknown as the BrownCorpus orCorpus). Each different manifestation of a word orsequence ofgraphic symbols(our atoms)wascounted asaunique entity. By 1982,theCorpus was reanalyzed in termsof unitscalled "lemma" and "lexeme". A sequence of graphic symbols was recognized asa"graphic word", where the constraining elements are spaces on either sideof the sequence of symbols. Each graphic word was assigned a tag indicating thegrammatical category towhich thegraphic word was assigned. Kucera and Francis then introduced the"grammatical word" which isthegraphical word with its tag. The concept of lexical word or "lexeme" was then introduced. The lexeme is defined as one or more grammatical words forming alexical unit,withthecriticalaspect that allmanifestation ofthe lexeme havea unitary meaning. Closely related is thelemma whichis the setof words having thesame stem/or meaning, and having thesame tag. 15 Lemmas can differ in inflection and/or spelling. In their 1982 treatise, FrandsandKucera providetwo majorfrequency lists; first analphabetical frequency list of lemmas and then a rank list of lemmas. Usingthesedefinitions,anL-meme isacombinationof graphicwords. In some respects,the Francis-Kucera lexeme and the L-meme defined in this paper are similar, although the lexeme concept does not imply replication. There exist a numberof interesting points in regards to WME which areworthwhiletobringoutat this time. First, some very usefulanddefinite metrics exist for published WME. Barschall62 recently examined costs per printedcharacter and impact (frequency with which articles in a given journal are dted). Barschall found that the average cost per printed character was the same in three fieldshe examined (physics, philosophy, mathematics),however costs within a fieldvaried. He also foundthat Rj the ratioof cost to impact variesbetween 0.063 to 54, with Rj forsdentific society publications beinglowestandRj forcommercial publishers being highest.Thesecriteria are beingusedby libraries tohelpdedde onjournal cancellations, an activity dearly critical in determiningthe rate of spread of scientificideas (and physical survival of specificjournal meta-memes). OthermetricsonscientificWME arederived from d tation analyses. These areused to evaluate and track the impact of sdentific papers, andare at times used for tenure decisions. A further justification for restricting the discussion to WME as opposed to SME, at this point, is the experience attained with automatic (machine) speech recognition. A significant amount of effort has been invested inthepast twodecades indeveloping machine speech recognition (MSR)6"6. The keydifficulties that MSR has tocontend with result from ambiguity, nongrammaticality, and wide variance in human speech (between individuals, and in speech of a single individual in different physical and mental states). MSR specialists havedeveloped multilevel classification schemes of different kinds. Isolated spoken word recog nition tasks are considered relatively simple, while connected speech recognition isquite difficult. A prindpal difficulty withconnected speech is the recognition of word boundaries. Unrestricted MSR, where the speakerdoesnotutilizespecial izedvocabulary andanevenspeech pattern is quite difficult to deal with. MSR systemstypically utilizeawidevarietyof knowledge about the speech inuse. Reddy63 discusses phonetics (speech sound characteristics), phonology (variability in speech sounds), prosodies (speech stress, rhythm, tempo, pauses, andintonation patterns), lexicon (sound patterns of words), syntax (grammatical structure) semantics (meaning of words andsentences), andpragmatics (context of conversation). The possible variety of these features is at present too large for acceptably accurate MSR of unrestricted speech. This experience in theMSR arena indicates the difficulty of constructing algorithms suitable foranalysisand testing of hypothesis in replicator dynamics of SME samples. This is not to say thatthereis nothingtogain, in fact SME analysis andtheoryis fasdnating and more reflective of memetic content in the "mind" or brain. It is the difficultyandambiguities involved that encourage postponement of this effortuntil asolidfoundation forWME replicator dynamics isdeveloped. 15 Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 V.2 ZipPs Laws of Language. Over half a century ago, George Zipf undertook a comprehensive examinationof statistical regularities of language. Due tohis encyclopedic treatment of many aspects of language, few people are aware of the key features of his two treatises "The Psycho-Biology of Language"24 and "Human Behavior and the Prindple of Least Effort"41. While many of Zipfs concepts ultimately require refinement, a set of his observations calls for restatement here. According to Zipf(and borneby manystatistical tests),word length and frequency of occurrence of words are dosely related. In particular increased frequency of word use is correlated with shorter words (i.e. smallerlettercounts).Zipfregarded wordlengthasoneofthemoststriking differentiating features. However, he did not ascribe the frequency of occurrence to wordlength.In his investigations he cameacrossa goodfit to the mathematical formula: ab2 = k (9) wherea is thenumber of wordsof a givenoccurrence, b is the number of occurrencesof these words and k is a constant. Zipf acknowledged this lawtobevalidforthelessfrequently occurringwords, withtheantidpation that thislaw would be applicable to 95%of the(different words) of any given sample. Afternumerous empirical curvefittings to largeamounts of textual material, Zipf enunciated what is now known as ZipPs Law 2^21,56*67: PM'J (10) where p(r) is theprobability ofoccurrence of ther-th word incommonness andA isa constant (which for reasonably sized samples =0.1). Mandel brot2*21 has shown that Zipfs law (eq. 10) can be derived from first prindples. Mandelbrot shows that ifone assumes that language isa finite Markov chain process (where after-effects of events have a short per sistence time), the exactrank-frequency relationship emerges: pW-PiB-l^-^r+Vy (11) where P, B andV are constants. Oneobtains equation 2 uponsettingP = 0.1, V =0 andB = 1.(An interesting aside that Mandelbrot points outis that Markov originated his stochastic approach to model linguistic processes). V J Information Theory, Entropy, and Channel Capacity. 16 The concept of informationand entropy in communicationtheoryas introduced by Shannon19,55,56'67 is not the same as the one utilized in thermodynamics and physicsin general.Entropyin physicsrepresents a measure of disorder. In assodation with physical processes entropy remains the same or increases (third low of thermodynamics), while in informationexchange processes(e.g. communication)entropydecreases. Clearlythere is a difference in the twoconstructs which requires darificationsince bothphysical and information entropyare of use to us in this investigation. Brillouin devotes anentire book56 to this topic. We adopt Brillouin's terminology here. Negentropy is a measure which reveals the possibility of a system doing work. Typically a system which has constituents at different temperaturescanbeusedtodowork,andissaidtocontainacertainamount of negentropy. Negentropy (N) is related to physical entropy S by the relation N = -S. Typically, corresponding to an increase of tsq heat, the entropy in a system increases by £S~&q/T (12) where T is the absolute temperature of the system (degrees Kelvin). Physical entropy S can also be interpreted statistically (asoriginated by Boltzman) in termsof the Boltzmanformula: S=*lnQ (13) where k is Boltzman's constant (138xl016 ergsperdegree centigrade) and Q is the number states the system can be in (given its constituent elements anditstotal energy). Theform of equation 4 is rather similar to the form utilized in information-theoretic entropy, and it is diredly the source of much confusion. The Shannon information entropy is in fact directly related to(and insome cases identical to) negentropy (-S). Brillouin categorizes information intoseveral kinds. Free information If occurs when the possible states ofa message areabstract (e.g. in the mindofanobserver)whereasbound information Loccurswhen itisrelated to physical manifestations. In this formalism, bound information is a special case offree information and itisbound information that isrelated toentropy (ornegentropy). A typical example ofBrillouin's definitions in our context is given below, A.A person possesses information (free information). B. Hewrites it down(bound information on paper) C. He transmits it via a telefax machine (bound information, subject to coding/decoding and transmission errors). D. Fax is receivedat destination and printed on paper (bound information). E. Another person readsthefax (freeinformation). F.Thereader forgets some information (lossoffree information). 16 Volume 1, Number 1 JOURNAL of IDEAS September 1990 In thisexample there isan opportunityfor lossof informationat every step of the process with the best case being no loss of information; the stepswhere we are dealingwith bound informationcan be connectedwith physical entropy. Note that there are a variety of physical mechanisms with which WME information can be obtained. Consider optical means (readingwith eyes), Braille reading(mechanical),computerscanning and voicingof text(optical/electrical/acoustical), anotherpersonreadingto us (optical/acoustic generation of speech). All these phenomena involve physical energyand entropy.Note, however, that entropycosts are low due to the minute value of Boltzman's constant. Thus, information exchanged physically can still take place and not impact macro-entropy directly. A key information theoretic concept is that of channel capadty and limitson information transferthrougha communication channel.Shannon and Weaver40 conceive of an information communication system as composed of an information source (which generates a message), a transmitter (whichsendsasignalcarryingthemessage), a communication channel (on which a noise source may act), a receiver (which receives a signal and translates it into a received message) and a destination. The message may be words, music, images, et cetera. A channel is fundamentally characterized by the amount of infor mationit can transmit per unit time.The key question in information and communication theory is what are the limits on information transfer for arbitrary(or specific)communication channels, with givennoisesources andmessage generators. Usingthe definition of channel capacity as: C = Lim \QgN(T) T (14) whereN(T)is thenumber of messages ofduration T,Shannon established thefundamental theorem fordiscrete noiselesschannels, namely that given a symbol source of entropy H (bits per symbol) and a channel with a capacityC (bitsper second),then: /. It ispossible toencode the output ofthe source insuch a way as totransmit attheaveragerateofC/H e symbolspersecond overthischannel (with e arbitrarily small). ii. it is not possible to transmit at anaverage rate greater than C/H. Inthecaseofcontinuous information (messages) andcommunication channels, andinthepresenceofnoise, therateofbinary digit transmission canbeshow to begoverned by the following channel capacity: Wlog^l+J) (15) where W is the frequency bandwidth of thechannel, P is average power used in transmitting thesignal and N is the average (band limited white 17 thermal) noise power. [Recall heretherelevancy oftheNyquist sampling theoremthatsays thata band limitedsignal,withfrequency range0 toW, and duration T, can be completely spedfied by 2TW numbers]. With the aid of Shannon's theorems, one can revisit earlier made claims about effidency of communication strategies which were con cernedwith the improved effidency of opticaland acoustical communi cationstrategies. It isdear herethatopticalcommunication strategies are optimal forhumans (andotherbiological organisms), ifa largeamount of information needs to be communicated (note, we are not discussing the value of information in this context). We take (conservatively) the lower limit to human audition as a frequency of 0 Hertz, and the upper limit as 31.5 kiloHertz(based on the upper limit spedfied in OSHA regulations), with ambientnoise being characterized as 35 dBA for areas requiring extreme quiet, and 100 dBA as the maximumtolerable human acoustic input (whichis alreadyabovesafety limits). Thesenumbers can be used to establish a maximum acoustic information channel input rate as 31500 logj(l + 100/35) per ear. The correspondingoptical limitscan beconstructed as follows:human visible range is approximately from 400 to 700 nanometers (violet to red). This corresponds tofrequendes of4.2-7.5 x 1014 Hertz, and abandwidth of approximately 3.3x 1014 Hertz. Even with marginal signal to noise performance, it isdear that thevisualcommunication channelcansupport significantlyhigherinformation transferratesover theacoustical. Thisby itself, is a dear reason why written/visual based systems are better than acoustically based systems, and why cultures based on optical systems will outperformand outdistanceacousticallybased systems. V.4 L-memes, WME, Meaning and Knowledge. In view of the foregoing discussion, it is dear that memes possess two key attributes. Accordingly,a more suitable definition for L-memes in the context of knowledge representation is: Definition 2:A memeisaninformational replicatorwhoseprincipal attributesare pattern and meaning. Definition 2 is a rather abstract definition of a meme. What is important to recognize here is that no dependencies are assumed or requiredonthephysical mediaviawhicha memeisexpressed or onwhich itis recorded. Forexample, considerthefollowingstringof letters inquotes "to be or not to be, that is the question". This meme[call it WSj] canbe understood when it is heard (acoustic encoding in air) or when read (material encoding inprintandlight/printedpageinteractions). Thememe can reside in someone's neuronal drcuitry, as a pattern of pits on a CD-ROM disk, or in magnetized domainson a floppydisk. Replication of thememeWS,occurswhenwe makea photocopy of a pagecontaining it, or a copy of the diskette or file in which it resides, and when we redte it or read it into RAM. WS] is easily seen to be composedof the memes "to", "be", "or", "not", "that", "is", "the", and "question". Obviously these eight 'simple' memesare insome waysless profoundthanWS!. However, they can still be regarded as memes (and in fact more successful memes than WS, since they get replicated more frequently). 17 Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 It is now useful to embarkon a strategyto investigate collections of simplememes. Todosoweneedtodefinethetermslexiconanddidionary. A lexicon is a collection of lexicalwords or lexemes.A dictionary is an ordered set of graphic words with associated definitions. The associated definitions are serially ordered collections of other graphic word entries in the didionary. Dictionaries can be static (i.e. have a fixed number of entries for all times), or dynamic ( new entries being added in order to improvedidionary and languageeffidency). In WME,graphicwordsare ordered strings made up of the letters of the English alphabet {a,..,z} & {A,..,Z}, the Arabicnumerals{0,..,9}and thedements of {-,', 'space'}. If we designate the i-th didionary entry (graphic word) as w,, then an L-memecanbe regardedasa particularorderedcollectionofgraphicwords which canbe denoted by Ma= {w,, w,2w,3wa4 w8„ }. The subscript n indicates the nth meme and the subscripts l..m denote word order. The wBj's may beanyof thedidionaryentries. Othersymbols maybedefined using the basic WME graphic words. Welook now fordirectly measurable quantities on L-memes in WME. Some very basic metrics are word counts and letter counts. Denote by WC(M,) the word count of the meme M,,and by LC(wlk) the lettercount of word wik. Consider now the meme Mj. The letter density [average numberof letters per word of Mj] is: PM) 1 »C(V,) WCM) & LC(Wii)' (16) One can calculate metrics on memes constructed from constituent memes. Consider the two memes M, and M,; one can construct a meme by concatenation, namely M,= M, ® HTheword counts addalgebra ically, i.e., WC(M.) = WC(Mr) + WC(M.). With theaidofequation (16) it is provable that: Pl(M,)<Pl(M,)+Pl(K)- (17) It is useful to construct entropy measures on memes. The Shannon information entropy template, H=-2 {Probability} log{Probability} can be extended to memes by considering the probability of WME word occurrences. With the use of P(w(j) as the probability of occurrence of word Wi,, thememe entropy isdefined as: wo/*,) H<Md- I ^K)log(PK)). /-i (18) It canbe easily shown then that meme entropies are additive, i.e., H(M,) =//(A/,)+//(A/,). The calculation of entropies of memes in KIPs forms a fruitful area of research. The probabilities of individual words depend onthe frequency distributionofwords inthe total corpusofwritten recordsat the time the calculation takes place. As soon as new text is recorded, the total corpus expands, allowing shiftsof frequency distrib utions, andconsequently changing meme entropies. Thusevenfora fixed memethe entropyof the meme can changein time.Furthermore, as new 18 words are created, entropies can change as well. This is where the substantive and interesting aspects of memetics begin to manifest them selves. The notion of meaning is very important and complicated. Ulti mately,meaningmustenterifwearetocorrectlydescribememeticspread. Here, we only sketch the beginnings of a constructiveworking [not final] definition. To define meaningone starts with dictionaries. A dictionary D(t) is a timedependent 'macro' L-meme. The particular ordering of the singlewordL-meme entriesinD(t)withassodateddefinitions [composed of L-memeentries inD(t)]is thesemantic networkthatembeds meaning in the particular connections of the associated definitions. This is essentially an obvious statement of consensus embedding of 'meaning'. Thedifficulty ofgenerally applying theconceptofmeaning liesinthefad that one has to search for 'meaning' in arbitraryL-memes, ratherthan in a codified [printed] single entrydidionary JD(t). Anoperational meaning of an arbitrary L-meme is obtained by decomposing the arbitrary meme into thesmallestnumberof multi-word sub-memesand indudng a virtual didionaryon thesub-memes. Theeffedive [operational] meaning is then thesequence of meaning imparted by theinduced virtual dictionary. It is this virtual didionary aspect that poses the problem and the inherent diversitiesand mutations that can occur. The decomposition of a complex L-meme intoconstituent sub-memes is a contextually depen dent constructive procedure that changes value when either a specific context embeddingchangesorwhenthedidionarieschange. Additionally, the virtual didionary is usually a purelymental, not a WME, construct whichis not recorded anywhere (hence, no consensus procedures could be applied, nor would there be time or resources to document virtual didionariesof all the KIPsinteractingwith the arbitraryL-memechosen). When particularly useful complex L-memes recur, didionary changes occur. These can be regarded as a meme-mutation to allow effident [Huffman like] encoding oflong compound memes into single word or low wordcount memes. It can be seen that the entropies assodated with new memesare lower than thoseof the definitions.Finally,it is dear that meanings are functions of the 'knowledge systems' that exercise thdr particular KIPs. Therefore, there is the high likelihood that different 'knowledgesystems' will impartdifferent meaningstothesame[complex] L-memes. While 'meaning' is difficult todefine unambiguously, thenotion of conceptset is more reachable. Thereason onewants todefine concepts is that memes reproduce, ingeneral, with a certain amount of mutation, yet they retain their meaning; ingeneral cultural analysis one ultimately wishes to deal with the replication of general systems of belief or knowledge rather than belimited tospecific instances. Thus, it is useful to definethe concept set S,as the set of all memes {My} havingthe samemeaning. Furthermore, there isa particularly important L-meme in S|called theunderlying concept. The underiying conceptC,isdefined as the first, lowest complexity element of S,. A practical measure of complexity isthe one ofTraub etAl67. 18 Volume 1, Number 1 JOURNAL of IDEAS September 1990 It is possible now to define structurescalled theories. Theoriesare constructed as ordered collections of concepts. A uniquely important theory is the idealtheory which is the ordered collection ofunderlying concepts, i.ê QltK - {UNDERLYINGSONCEPTS,^ - {C/(JC}. Typical underlying concepts that would occur in ideal theories indude: 1) rules of combining CI(K, 2) didionary definitions, 3) hypotheses andtheorems, 4) axioms, and 5) auxiliary terms. Ultimately, theories (which are loose connections of concepts) evolve and combine to become ideal theories expressed in terms of underlyingconcepts. V.5 Knowledge Systems, Knowledge Acquisition, Learning and Discovery. It is dear that when there exist interactions or transactions between knowledge agents,a knowledge systemisoperative. Ageneral knowledge system(KS) is a systemcomposed of a memory subsystem, a knowledge acquisition subsystem, a knowledge processing subsystem and an input/output subsystem. These subsystems individually andcollectively engage in KIPsandrequire knowledge representation (KR)capabilities. A knowledge system is usually a computer basedelectronic system or human based system [with one or more human agents]. Two principal mechanisms of knowledge acquisition by independent systems are learning and independent discovery. Learning can be shown to be a particularcaseofmeme-replicatorspreading. Discovery ischaraderized asapplication of KIP rulesto knowledge entities already acquired by the knowledge system. A measure thatcharaderizes a knowledge system is total knowledge. When two or more independent, dissimilar knowledge systems interact, total knowledge of the combined system can increase andbelarger than thesumof theindividual non-interading systems. The onlyway for total knowledge to increase through interaction of twoor more KSs is to have copying [read replication] of knowledge between systems and knowledge combination (new meme construction). Rein forcement (i.e.copying of knowledge already present inboth systems) is something that can and is usually accounted for. In KSs that allow for value-assessment, an L-meme thatis reinforced byan objective KIPwill usually have greater value. Advanced KSs may have rather developed mechanisms for discovery, in this case, there typically arebuilt-in reward functions for construction of theories and ideal theories. Computer viruses satisfy theconditions of being replicators. When regarded as symbolic codes, computer viruses alsosatisfy the condition of being electronic memes that can mutate in a way similar to general meme replicators. These electronic memes can then also bedescribed by theequations expressing meme mutation andspread. Meme mutations arereflected inchange ofdimensionality of thememe phase space which is used for knowledgerepresentation. TheL-memes discussed here started with an implidtassumption of 'atomic' or fundamental units. Combination of primitive memes yield complex memes. A sequence of increasing complexity memes is: sen tences, paragraphs, chapters, books,librariesetc.Withregard tocomputer oriented replicators, one can look at hierarchical levels of data record 19 entries, records, databases, collection of databases, machine level instructions through highlevellanguages andpseudo-codes. Allthesecan be interpreted via the memeformalism. In this context one needs to mention that the replication aspectsof L-memes are precisely those that are required to formulate a basis of evolvingartificial intelligence. The conceptsof replicators and memes have been shown to be of highvalue in describinggrowth, mutation, and selection processes in biological and ecological systems. As interacting AI(Artifidal Intelligence) systemsbecomecapableof learningfromother systems along with the informational environment (in a non-trivial manner), the calculus of concept acquisition and knowledge acquisition will require the type of knowledge replication and spread calculus described here. or 29 thttlT not 16 with IS thoy14 113 for 12 itn to 10 hsvo9 to 8 r»7 In 6 a5 and4 0(3 bo 2 thsl i i t 4 • • 7 • • ton tan 14it it ir tin to Figure 2 Trajedory representation of the meme "to be or not to be". The ordinate entries are the rank ordered lemmas of the Brown Corpus, theabsdssa entries are thememe [word] entries according to their sequential order of occurrence in the meme. V.6 Memetic Phase Space. Oneof themorepowerful techniques forvisualizingorganization and development is the use of phase-space descriptions. In section V.4 the syntadic form for denotinga memewas introduced. In order to describe memesviathephase-spaceapproach, a particularorderingofbasicmemes is required. Wewill initiallyadopt theword-rankingcalculatedby Frands and Kucera in theirmostrecentre-analysis of theBrownCorpus[ref.61]. The basic L-meme building blocks used will be the lemma (where, for 19 Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 example, 'be', 'am', 'are' and 'art' are different inflections of the lemma 'be', while theL-meme 'to' hastwotags: thefirst onebeing a being an infinitive mark 'to,'and thesecond 'tOj' being a preposition). The ordinate axis of the memetic phase plane is constructed by enumerating theFrancis-Kucera lemmas according to their ranked [ad justed] frequency of occurrence [in theCorpus]. Thusthe null-lemma or null-meme is represented by theordinate valueO, thelemma 'the' (which is themost frequent word in theCorpus [and in theEnglish Language]) has rank land ordinate value 1, etc. Theabsdssa denotes the serial location of occurrence of a particular lemma in an arbitrary L-meme. Toillustrate the construction of a meme phase-space portrait, consider the L-meme 'to be or not to be'. The lemma 'to' appears in the first and fifth serial location of the meme, 'be' occurs in the second and sixth locations, etc. One couldalso use the syntadical description [8,2,29,16,8,2]to describe 'to be or not to be' unambiguously. The pidorial representationof 'to be or not to be' is given in figure 2. A veryinterestingfeatureof describingL-memesvia thisphase-space approach is the immediacy of entropy/Information calculation. By combining equation 18 and Zipfs Law (equation 10), and notidng that the ordinate value of the i-th lemmain an L-memeis the rank required as input into Zipfs Law, a Zipf-information measure can be calculated for arbitrary L-memes, namely: wcwa A i-\ r r (19) Thus,one has a directly calculableinformation measure. From this discussionone noticessome interestingtopicsforfutureresearch,namely: i) thecomparisonof the Zipf-information to the true informationvalueof a meme (which takes into account all WME in existence), and ii) the samplingbasedestimation of true WMEentropies, given thatin realityit is impossible to have access and summarize the totality of all written material in WME. V.7 Memetic Hierarchies. In dosing thissedion on language basedmemes, onemustmention that thereare obviouslyhierarchiesof memes.In the mannerthat one can regard hierarchies in biological organization andsodety, one hasequiv alent scales of hierarchies in memetic structures. Table 1 provides a summary hierarchy tabulation for four categories of entitiesand rough correspondences. In this context, we use L&W's4 term euculture ".. advanced form of culture, in which individuals not only teach and learn information, but alsoconceptualize muchof it into concreteentities that can be more readily labeled by symbols and handledby language." We also introduce here the concepts of trans-culture and Homo trans-sapiens (or simply trans-sapiens). While being topics of a future paper, trans-culture canbedescribed as thenextstepofculture dominated by deep connections, interactions, and relationships between objects created by large human/machine teams. A manifest propertyof transculture is the extreme and transcendent complexity of interactions and 20 relations between humans and the cultural objects involved, with the additional property of being non-accessible toHomo sapiens. Examples of trans-cultural objects already exist; forexample, thereis noindividual who(atanygiven temporal instance) isanexpert inallaspects ofmedidne, orwhois familiar with allbiological spedesandthdr relationships, or is anexpert inallaspectsofphysics, orwhoistotally familiarwithallaspects ofevenasinglecultural artifad(e.g.Hubblespacetelescope, SpaceShuttle design, or the total design of a nuclear power plant). In fad, we are approaching the point that certain proofs of mathematical theorems are becomingtoolonganddifficultforanyoneindividual to keepinconsdous awareness. In a way, these transcendent and extended complexity rela tionshipsare examplesof morecomplicated 'meta-memes',whichis one of the reasons it is interestingto study the evolutionof ideas. Ecological Sequence Cultural Sequence Homo Sequence Memetic Sequence atoms no culture no human letters molecules morphemes chains proto culture proto human words cells parts of sentences organs culture Homosapiens sentences individuals paragraphs spedes euculture chapters ecologies books grand ecolo gies libraries trans ecologies transculture Homo transsapiens hypertexts, hypemets, electronic megadatabases Table 1. Hierarchies in biological organization,cultural evolu tion, human evolution, and memetic complexity/organization. The correspondences are roughat this point. Homotrans-sapiens is the [postulated] nextstepinevolution of homo sapiens. There is no reason to expect or require that Homo sapiens will not undergo further evolution. The bio-historical trend indicates that the major evolutionary development in Homo is in the cortico-neural arena (i.e. increasingly more complexorganization of the nervoussystemand the brain). Spedfically it is the higher level cognitive-KIP functions that 20 Volume 1, Number 1 JOURNAL of IDEAS September 1990 set H. sapiens apart. It is asserted here (and to be discussed in a future paper) that H. trans-sapiens is a logical consequence of evolution, and that the milieu and adaptive epigenetic landscape for//, trans-sapiens is already present in the form of trans-culture. It is indeed possible that the basicmutations areinplaceandtrans-sapiensalreadyexistsorwillappear in the biologically-near time frame. VI. Memetic Spread Equations. Earlier,memeswerearguedtobea particularcaseofreplicators. Basic replicator equations were discussed and a representative case of two spedes predator-prey was articulated (equation 7). Unfortunately, the previously discussed replicator equations [section IVandreferences 4,12, 15-18, 28] are not sufficiently developed to yield practical results that supportand extendthe memeticcore program (sectionV.l). Weassume that thecontext of discussion is that wehave a large set (or population) of Knowledge Systems. If we denote by KS,the i-th Knowledge System, and regard it as being composed of {Input/Output channels, Memory Store [that stores memes received through the I/O channels as well as memes generated internally, and also stores other internally or externally generated sense traces], and a Processor that executes knowledge/information processes [KIPs]}, we can pose the following quantitative questions regarding meme evolution and spread: Q.l: Given that ameme M,originates inKnowledge System KS„ when does thememe M, arrive atanarbitrary KS,? Q.2: Given a state configuration of all Knowledge Systems at time t (i.e., a detailed description ofthe memory store ofall KSs), what is the state configuration of the KSs at some future time t*=t+ n&t (i.e. n time intervals later)? Q3: How many, and which KSs accept meme M; as 'true'? Inorder to answer these questions aninteraction model is required. Reasonable starting points arethefollowing ansatzs: A.1: When two Knowledge Systems KS, and KS, are withinsome 'distance' d,j from each other they will communicate (or interact) spontaneously at some time, with increasing probability as timegoeson. A.2: The relative probability that a particular meme Mk is communicated byKSj depends on the internal complexity of the meme, its relative acceptance state,and the number of times KS, received the meme. 21 A3: Any meme or set of memes can undergo mutations and combinations. These mutations/combinations are internal KIPs of a Knowledge System. A.1 is usually evident when the KSs are humans and the mode of interaction is speech (e.g., SME). For example, when two adult humans comewithinsome thresholdgeometricaldistance, the probabilitythatthey will interact will grow with time and increase with decreasing distance. A probability of interaction between KS, and KSy can thusbe written as: Pl^C^,t"\ (20) Here the parameters ml and m2 need to be determined by dimensional analysis; Q and a are constants. Note that at this time no particular assumption is made concerning the number of connections between Knowledge Systems, norisany linear, planar, hyper-linear or hypercubic assumptionmade.Itwillbe useful laterontoimposeparticulargeometries, such as linearchainsor Isingspin typemodels, tomakeactualcalculations tractable. One can express the relativeprobabilitiesreferredto in A.2 usingthe partition function formalism of statistical mechanics. The relative prob abilityof memeMk beingcommunicated can thenbe givenas: P, w,e -HfiT lw(e -HJkT' (21) where Hj incorporates acomplexity metricandotherenergy costs, andthe weighting fador w, incorporates the relative acceptance state (accep ted/believed, rejeded asfalse, nojudgement,etc.)andthenumberoftimes aparticular Knowledge System has been exposed tothe meme inquestion. Theconstant k is Boltzman's constant while T is a parameter that plays the role of temperature, and represents internal noise or fluctuations internal toandexternal to theKnowledge Systems. A.3 is a general statement reflecting the evolutionary aspects underlying allofmodem biological thought. Itspractical application with respect tostrings of symbols is manifested in Holland's development of theories ofadaptation innatural and artificial systems and the particular implementations in the Genetic Algorithm techniques for solution of search problems w. Equations 20 and 21, and the realizations of suitable mutations are the elements required for proper meme spread equations. Theauthor's paper "Memetic Science: IIMeme Spread Equations"70, inthenext issue ofJ ofI,will present the next step inthe development of these equations. There, the formalism of the Einstein A and B coefficients forderiving probabilitiesofspontaneousandstimulatedtransitionswillalsobe utilized in the struduring of the memetic formalism. This approach will allow accounting for both learning (stimulated transition) and discovery (spontaneous transition) in terms of the metrics on memes discussed in section V. 21 Volume 1, Number 1 Moritz: Memetic Science: I General Introduction September 1990 References. 1. K. E. Drexler, Engines of Creation, Anchor Press/ Doubleday, New York, 1987. 2. R. Dawkins, The Selfish Gene, Oxford University Press, New York, 1976. 3. R.Dawkins, The Extended Phenotype, Oxford University Press, New York, 1982. 4. C. J. Lumsden and E. O. 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