What’s Memetics, Game Theory, Free Will, and Transfinite Math Got to Do with It?

“What’s love got to do, got to do with it? What’s love, but a sweet old-fashioned notion?” -Tina Turner

I’ve previously spent a lot of digital ink exploring the nature of love. And I’m fairly confident that most of what I wrote holds together and offers a nucleus of wisdom or ethical knowledge, with a platinum and golden rule at the core. But humanity has been discussing the nature of love for millennia; the real task seems, to me, not just to establish a firm and credible and inspiring sense of what love is, but also to establish some firm theoretical connection between this wisdom and the realm of hard science and analysis and math. After all, it’s in the hard sciences, analysis, and math that human beings seem most able to set aside their egos and really get to work combining knowledge to build up seriously durable models of reality; if our age can contribute anything to the age-old discussion of the nature of love, it would be an understanding of how love-and not just animal affection or lust or kin-based quasi-altruism, but real, fully rational, paradise-propagating love, as described in my other posts-can be explained in terms of mathematics, hard science, analysis.

To arrive at this lofty goal, we must first ask a seemingly unrelated question. I.e., what sets us humans above other animals, other species on earth? How are we any different, and is the difference qualitative or just a matter of degrees? In other words, as the oracle would have us ask, “What is man?”

Certainly, the more we open our eyes to our fellow Earth species, the fewer traits we’re able to claim as exclusively human. Gorillas and elephants mourn; elephants, jaguars, and ants use mind-altering drugs; chimps enjoy painting; termites build skyscrapers, army ants build bridges; chimps laugh; dolphins act altruistic toward other species; chimps wage war with weapons, dolphins attack sharks for fun; birds prostitute themselves; dolphins use complex syntax, probably; insects farm; great apes, elephants, orcas and magpies recognize themselves in a mirror; crows create tools spontaneously to solve problems they’ve never before encountered.

And so on. But consider the scale at which humans do what they do, the speed with which they develop adaptations, the scale and complexity at which they soon arrive in each adaptation. Yes, termites build termite-scale skyscrapers, but they’ve been building the same kind for millions of years. Humans figured out how to build their own skyscrapers only a century ago, and they continue to double in volume and multiply in styles at an unbelievable rate, even as the number of skyscrapers continuously grows. Likewise, many animals ingest medicinal plants for medicinal purposes, but none of these species show anything like the pharmacological acumen of even the most isolated Amazonian shaman.

There’s something almost beyond exponential about the human growth rate, the human learning curve, the human mutation rate. But how could that be? We can certainly imagine a graph of a growth curve steeper than any exponential curve-for the sake of argument, we can call this sort of curve hyperbolic. Where x is time and y is the factor changing over time, such a hyperbolic curve approaches infinity in a finite time; at a given point x, y = infinity, with a vertical asymptote at x. While this curve is easy to conjure, it’s hard to imagine any sort of real-world hyperbolic growth, for we have no experience of infinity anywhere in nature. The most we can imagine, based on our experience, is the indefinite-a real-world process or an entity that can continue indefinitely, because it has no built-in limit on its endurance.

What Memetics’s Got to Do with It

I believe humanity’s unique adaptability, growth, power, and promise all stem from the fact that humanity is defined not just by the usual replicator-genes-but just as much by a second replicator-memes. Memes are units of human language meaningful to a community of human beings. Memes can meet all the same criteria for replicators that genes do, but with a serious catch: memes are not absolutely fixed in form. In any given context, yes, a meme is as concrete and non-negotiable a unit as a gene, with a particular shape, a particular medium, a particular size, a particular function or range of possible functions. And it is thanks to this solidity, this particularity, that a meme qualifies as a replicator, as a building block of the sort of game we call life. But a meme can do something that a gene cannot: it can transcend. For example, the word “water” can be translated into the word “agua.” Or the spoken word “water” can be represented by the written word “water.” Or the handwritten ink-on-paper symbol “water” can be copied into typewritten form, or typed in a word processor, so that it exists as unlit pixels on a screen and as binary code on a hard drive. The font of a word can be changed, as well as the size; an alphabetic word like “agua” can be translated into a hieroglyph or into an ideogram. A word can be carved into stone, or turned into radio waves, or turned into electric pulses or fiber optic pulses. All without losing its meaning, its ability to serve a similar function in multiple hosts or carriers or vessels or minds. This is what I mean by saying a meme can “transcend.” Elsewhere I define “spirit” as translingual and transmaterial content. By that definition, one could well say memes are more spiritual replicators than are genes.

Because memes can transcend, or are more spiritual, they are indeed more indefinite. Genes have built-in limitations on their endurance, because they only exist in one form, one language-DNA-and this form inevitably breaks down in the presence of radiation; inevitably breaks apart at temperatures slightly higher than in our biosphere and inevitably stops moving and working in temperatures much below the freezing point of water; inevitably, therefore, cannot possibly endure for more than a few billion or trillion more years, depending on whether the universe collapses in a big crunch or expands into a frozen emptiness. Memes, by contrast, are real-world entities with no built-in limits on their endurance, based on what we’ve seen of their mutability, their spirituality, their lingual and material transcendence.

Because memes and genes differ in this regard, they represent two distinctly different forms of life. But “forms” is vague; I don’t mean they have different shapes, or exist in different media; what I really mean is that they are two distinctly different games of life.

What Game Theory’s Got to Do with It

Game theory seeks to formalize or mathematize goal-oriented, purposeful, teleological activity in order to arrive at general truths about such activity; it is the science of goal-oriented activities or “games.” Each game is defined by the presence of at least one goal, one boundary or limitation or rule, and one player. The game of climbing Mt. Everest, for example, requires reaching the summit of Mt. Everest (the goal), getting there alive (a rule) and using your own muscle power to do so (another rule), and it also requires that someone be the climber (the player). A second example: The game of splitting a cake evenly between two people so that both deem the split an even one (a classic game theory example) requires, what else, splitting a cake evenly so that both recipients deem the split an even one (the goal), not deceiving either player about how much cake there is to start with or how big the split pieces are (a rule), and it also requires that at least one person do some cake cutting and that two people do some cake-slice fairness-deeming (the players).

Game theory is relevant to the memetic and genetic forms of life because both these forms of life fit game theory’s definition of a game-they are defined by a goal, rules, and players. The goal of both forms of life is perpetuation. Both forms of life are likewise bound by rules or limits, such as the incompatibility of certain memes or genes, or the need for memes and genes to be expressed in particular media. And both forms of life are defined by the presence of players-genes and organisms in genetic life; memes and persons in memetic life.

What Free Will’s Got to Do with It

Note my distinction between genetic life’s “organisms” and memetic life’s “persons.” Genetic life is goal-oriented enough to fit the definition of a game, but as most biologists will be quick to assert, genetic life’s players are not purposeful, are not mindfully pursuing a goal of perpetuation. We speak of what the amoeba wants to do, but we don’t imagine for a moment that the amoeba has a mind at all. But we’re often haunted by our inability to explain exactly where on the spectrum of biological complexity this “mind” or “purposefulness” appears.

I submit that in genetic life, as in any game, there must be at least one real player, one agent whose function is to weigh multiple branching possibilities in order to determine which ones lead closer to the game’s goal. The catch is: in genetic life, the organisms in large part serve not to weigh such possibilities, but to be the possibilities weighed. Genetic life’s method, natural selection, actualizes every possibility in order to weigh its viability. Every variant individual organism that genetic life brings into existence represents one possible route leading closer or less close to the game’s goal of perpetuation. Hence the blindness of natural selection to individual organisms’ suffering and death-suffering and death turn the wheels of genetic life’s calculations. The calculating mind behind genetic life, is a gestalt of the entire planetary history of natural selection. We might, in keeping with my definition of “spirit” elsewhere, call genetic life’s one real player “the spirit of genetic life.”

If this concept seems foreign to our basic understanding of games and how they work, it’s because we are used to thinking of ourselves as game players the way we’re players in the game of memetic life. That is, we’re used to thinking of ourselves as real players, agents who serve to weigh multiple branching possibilities in order to determine which ones lead closer to a game’s goal. Memetic beings model, within themselves, multiple futures and determine where in these virtual, imagined causal chains where they can, by their actions, make some futures more likely than others, and then they act in such a way as to make more likely the futures that lead closer to their goals. Note that this process is synonymous with “choosing” or “having free will.” Note that this process presupposes a power of imagination great enough to model more than one future and great enough to see how these futures could be affected by one’s own actions. The ability to model multiple future worlds with such facility and such power of prediction requires that the models be made of something extremely dense or condensible and extremely flexible and yet extremely reliable. This something is the “meme.” The ability to relate these modeled futures to one’s own modeled self, to determine how one’s actions can lead to one future or another, is synonymous with our prized virtue of “self-awareness,” “sentience,” “consciousness,” “ego.” Note that without the ability to imagine more than one future, or the ability to imagine accurately one’s self, one would not be capable of free will or choice. And note that it’s the meme that enables these imaginative feats of accurate modeling. If you doubt it, consider that our ability to model complex dynamic systems such as hurricanes with any accuracy has advanced in direct proportion with our ability to build such systems out of language-in this case, mathematical language and computer code. And consider the following statement from Helen Keller, in support of the idea that accurate self-models are built of memes: “When I learned the meaning of ‘I’ and ‘me’ and found that I was something, I began to think. Then consciousness first existed for me.” If you require testimony from a different sort of authority, consider Darwin’s assertion from his Descent of Man: “If it be maintained that .. self-consciousness, abstraction etc. are peculiar to man, it may well be that these are incidental results of other highly-advanced intellectual faculties; and these again are mainly the result of the continued use of a highly-developed language.”

To recap: memetic beings model, within themselves, multiple futures and determine, using a self-model, where they can by their actions make some futures more likely than others, then act to make more likely the achievement of their goals. In genetic life, if these branching possibilities are modeled at all, it’s not in any organism’s imagination; each possibility is acted out, is lived, as a distinct player. Thus genetic life’s dependence on redundancy and waste and death to effect adaptations.

It probably bears mentioning that in the above section I’ve managed to define free will as well as come pretty close to pinning down the difference between humans and animals.

And I’ve got a whole bag of booyah with your name on it.

What Transfinite Math’s Got to Do with It

It’s all well and good to say, as an armchair theorist, that genetic and memetic life can be defined and analyzed using game theory. However, attaching actual math to these particular games can be tricky, for one or several reasons, depending on how you look at the tricky part.

For starters, even with the simpler game of genetic life, we find that the goal-perpetuation-is open-ended. One way or another, this means genetic life’s goal is infinite. And infinity is a tricky quantity to incorporate into mathematical formulations. Still, while for genetic life’s one real player, the goal is infinite, for each organism and gene the goal is easily defined in less exotic terms-replicate oneself, or most of one’s genes, as much as possible before inevitable death, or more than one’s competitors, or at an optimal rate for long-term perpetuation. Of course, at the point where an organism is reproducing at rate optimal for long-term perpetuation, it’s acting wholly in the interest of that one real player, but eminent biologist Richard Dawkins could have told you, all organisms actually act not as though their own players trying to win their own finite game, but as pawns of the almighty gene.

While genetic life lends itself to at least some mathematical description and analysis without introducing infinite terms, with memetic life such is far less the case. And the reason comes down to the meme’s profound collapsibility. See, genes are bulky, as replicators go; each nucleic acid requires a certain number of atoms of certain chemical elements, has a certain mass, has a certain inherent vulnerability to radiation, takes up a certain amount of space, and so on. In fact, it’s these qualities of genes that force them everywhere to compete for space, resources, and the chance to replicate. And as is well-known, it’s this competition that drives natural selection. Dawkins’ definition of a replicator, and thereby of a life-game, requires such limits or boundaries or rules, and thus does genetic life supply them. In fact, it’s because of the definite, finite, and vulnerable qualities of genes that death comes so inevitably to every organism acting as vessel to them-sooner or later, an organism’s copies of the genes get corrupt, and in terms of genetic life’s one real player, their constituent atoms would be of most service if broken down and reassembled into a new copy of said genes and gene-support-systems. This deadly logic is so airtight, nature has even seen fit to equip each multicellular organism’s genetic code with telomeres, genes that, like the three Fates, determine the life span of each cell line and ensure the eventual death of each organism.

Memes don’t work quite the same way. Memes somehow accomplish evolution-and act as a form of life-without having a certain mass, an inherent vulnerability to radiation, a certain volume-or rather, they do have such limitations, but only in small contexts. That is, memes always take on conventions, but are beholden to none.

For instance, memes are not inherently competitive. Memes behave as though they can’t run out of space-at least, if you look at the history of their evolution, which we conveniently call “history,” as opposed to genetic life’s “prehistory.” And this doesn’t seem to be a case of memes simply growing and diversifying exponentially until they reach the limits of their space. Instead, memes seem to be indefinitely collapsible, condensible. The number of memes that once fit on a clay tablet can now be condensed to fit on an invisibly thin string on a computer’s hard drive. And before information theorists object by saying there’s a limit to how much longer memes can continue to condense, consider that memes are also semiotically collapsible-consider for instance the vast swaths of information that can be referenced by the word “Iliad” or “M theory” to a user who has read the text referred to by the term. Or for a more ultimate example of a collapsed meme, consider the term “infinity” or “the set of real numbers.” If this doesn’t make memes seem collapsible enough, you might also consider the possibility that the same memes that lead us humans to be so thoroughly inventive, may one day enable us to invent space at will.

In fact, in a very valuable sense, memes already do this. If so far my description of memes and genes’ differences doesn’t seem to explain my sharp distinction between the two as forms of life or replication-game, please refer back to my definition of free will above. Where genetic life has no ability to model possibilities other than to actualize each one, each memetic being, in direct proportion to its memetic richness, is able to create multiple virtual worlds inhabited by virtual versions of itself and its neighbors. This process is known as imagination, and whenever it is used to determine which action is most likely to get the memetic being closer to a goal, it is known as choosing or the exercise of free will. The reason for repeating this again is to point out that such a process, insofar as it produces accurate models of reality, invents virtual space at will. And it does so solely due to the collapsible nature of the memes out of which the models are built. And by collapsible, I emphasize that I mean more than simplifiable; I mean that a very small term can stand in for a vast amount of information without losing fidelity to the complex reality, the vast amount of information, to which the term ultimately refers.

So memes do, in each particular manifestation, struggle against limitations, and do exhibit the process we call evolution or life. But they are bound by no particular limitations, and in fact seem to make possible the collapse of any or most possible game limitations. The upshot: the memetic form of life promises to offer its players a better game than the inevitable death and inescapable competition of genetic life.

Still, unless memetic life can offer its players individual immortality, it’s really not qualitatively different from, or better than, genetic life-the goals are the same in both games-for the replicator vessels, a small finite victory of replicative success relative to one’s neighbors, and for the spirit of the game, perpetuation of life and suffering and death. But it’s one thing to say memetic life seems more unbounded, more indefinite, than genetic life; it’s another to assert that it could actually offer to be an infinite game for its individual players. After all, we’ve never seen infinity, and even talking about infinities in mathematical terms such as game theory strives for, leads to absurdities galore.

Not so fast, though. We’re forgetting about a little branch of math called transfinite math. Developed by a guy named Cantor, transfinite math allows us to distinguish between different sizes of infinity, and therefore to analyse infinities with formal language that doesn’t always result in answers of infinity and 1/infinity. In other words, Cantor’s transfinite math means we could, through game theory, study the possibilities of infinite games without having to take out a mortgage in cloud cuckoo land.

The real problem with proposing the possibility of an infinite game isn’t that people will think you’re crazy. The real problem is that when we confront the possibility of infinity, we experience existential nausea, or vertigo-we stare into the abyss and it stares back into us. By making infinities relative and manipulable, Cantor’s transfinite numbers allow us to imagine how an infinite game could have structure and purpose and interest.

But for an infinite game to have structure, purpose, and interest, it has to have some unifying or overarching goal other than perpetuation. (If the goal is perpetuation, then death is possible in the game, and the goal the escape of death-and then we’re back to talking about a game like genetic life.) And since an infinite game is eternal and infinitely variable, the unifying factor of an infinite game must itself be an infinitely powerful strange attractor, capable of unifying infinite varieties-though not all possible infinities; some possibilities will be outside the boundaries of the game because they disrupt the infinitude, or unity, or purpose of the infinite game. (This is all to the good-even an infinite game needs some boundaries in order to qualify as a game.)

Hence the not-uncommon intuitions that eternal life-an infinite game-would have a unifying focus or God, as well as an outside, a boundary to it. If you wonder why an infinite game has to have unity, well, it doesn’t-but if it’s non-unified, it has a hyperbolic curvature, like a spacetime fabric with hyperbolic curvature, expanding forever until everything in it becomes an irretrievable island. For a fine imagining of such an eternity, see C.S. Lewis’s vision of hell in The Great Divorce. Or consider the transience of a “random walk” in 3+ dimensions.

Ren takes a random walk in three dimensions, develops space… madness.

So we’re imagining essentially an infinity with a center or goal, and a boundary or boundaries. This seems a strange object to try to imagine, like a house bigger on the inside than on the outside. And indeed, perhaps the strangest thing about goodness and God and beings with free-will and the memetic game they play is that these things are bigger on the inside, more interesting on the inside. Consider again the worlds upon worlds imagined within each memetic being. Or consider, as an analogy, the Mandelbrot set: an object of infinite complexity and density, it rests in an infinitely larger space without feature or interest-the black background in the image below.

“…We could explore space, together, both inner and outer, forever, in peace.” -Bill Hicks

The deadliness of the genetic game means organisms and genes cannot afford to break free of self-bias. And so long as this bias is present, pure rationality and love are not possible. With the meme comes the possibility of a truly better life, centered on the love described in my previous posts. But it’s no mean feat to overcome the billions of years of genetic hardwiring in each of us that predisposes us to believe only in the genetic type of replicator game, and to adhere only to its assumptions and rules. If memetics, game theory, an understanding of the nature of free will, and transfinite math can help us, it’s by giving our better hopes the backing of science and the relative confidence science can give us.

One might object that science can have nothing to do with spiritualistic conjecture. However, if memes are able to transcend material and form while still carrying the same information and still behaving as replicators, then they are, according to my definition of spirit, a more spiritual replicator-i.e., their content is transmaterial and translingual. Everything else described above simply follows. Well, not simply.

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4 Responses to “What’s Memetics, Game Theory, Free Will, and Transfinite Math Got to Do with It?”

  1. » Blog Archive » Love Gone Platinum: Rationality and the First Two Laws of Love Says:

    […] its best developments (e.g., multicellular, thinking genetic selves) entirely in moving into a new order of complexity (e.g., multicellular, thinking memetic-genetic […]

  2. » Blog Archive » Harmony & Diversity: Joy, Collective Love, and the Two Ends of Love Says:

    […] to share something we enjoy, marks a boundary between selfish pleasure and something more divine. When we can give something without losing it, when we can have something without fearing its loss, we don’t hold back from sharing that […]

  3. Kelley Says:

    Re “Note that without the ability to imagine more than one future, or the ability to imagine accurately one’s self, one would not be capable of free will or choice.”
    If you only consider one action at a given moment and that action seems right and it’s the one you go with, are you not practicing free will?

    Re “Memes somehow accomplish evolution–and act as a form of life–without having a certain mass, an inherent vulnerability to radiation, a certain volume–or rather, they do have such limitations, but only in small contexts. That is, memes always take on conventions, but are beholden to none.”
    They always require at least one (from the Cartesian cogito-ergo-sum position) or two (from the Berkley-an esse-es-percepi position).
    I can give that memes seem to can move about more dynamically, but they still need surfaces on which to move.

    Re “The upshot: the memetic form of life promises to offer its players a better game than the inevitable death and inescapable competition of genetic life.”
    “Better” if what exactly is the goal?

  4. » Blog Archive » Recipe for Heaven Pt 2: Steps Says:

    […] 5:  Use my definition of free will from the post “What’s Memetics, Game Theory, Free Will and Tr… to determine which of the soul’s actions, and to what extent, were the result of free will.  […]

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