Fractals and rhizomes for dinner tonight.
Mise en abyme at lunch on Thursday.
Fractals and rhizomes for dinner tonight.
Mise en abyme at lunch on Thursday.
Regarding the possibility of the Earth remaining hidden from detection by alien civilizations by running silent, New Scientist points out that it’s already too late (Shostak, Seth, “It’s Too Late to Worry That the Aliens Will Find Us,” 3 July 2010):
We have been inadvertently betraying our presence for 60 years with our television, radio and radar transmissions. The earliest episodes of I Love Lucy have washed over 6,000 or so star systems, and are reaching new audiences at the rate of one solar system a day. If there are sentient beings out there, the signals will reach them.
(Related: “The Noosphere Visualized,” 1 January 2009)
Arms racing is the suboptimal outcome of a prisoner’s dilemma (all competitors feel compelled to over purchase security).
The prisoner’s dilemma is created by absence of coordination among competitors with a shared interest (states are better off planning for national security according to real rather than systemic considerations [though I’m not sure that the real/systemic distinction is tenable — at some point the system is the real]).
Arms control is the coordination among strategic competitors that allows an escape from the best-bad outcome reasoning of a prisoner’s dilemma.
My friend Mick alerted me that Carl Zimmer was featured in a recent episode of RadioLab dedicated to the subject of parasites (Abumrad, Jad and Robert Krulwich, “Parasites,” 7 September 2009). Despite being somewhat annoying in format and low-density in it’s information presentation, the show contains a number of points interesting to my project.
In the second part of the second segment (starting at 31:25), they deal with the symbiosis between hookworms and the human immune system. The segment consists of a profile of Jasper Lawrence, a man who had severe allergies and — having chased down a certain direction of research — decided to travel to Cameroon to infect himself with hookworms. The research in question is that of the hygiene hypothesis: the notion that many developed world afflictions, including allergies, result in part from the excessively sterile human environment. Asthma is 50 percent less likely in a person who has had a hookworm and in Africa allergies are almost entirely unknown. It is theorized that similar to the dependence of digestion upon a symbiotic relationship with non-human microflora of the digestive tract, the immune system is dependent on certain microorganisms for regulation and calibration of the immunoresponse. The complex chain of events that is the immunoresponse evolved in the constant presence of parasites, evolved around parasites; they have co-evolved to the point where their presence became necessary. “We function like rainforests; we’re ecosystems,” Mr. Lawrence says. This is the hypersea washing through humanity.
The final segment is on Toxoplasma Gondii (starting at 47:55), a parasite that lives in cats and makes their feces dangerous to pregnant women. Like many parasites, it has a multi-phase lifecycle that takes place in a multiple hosts. It only reproduces in members of the Felidae family (cats), but can live the remainder of its life in any warm-blooded creature. T. gondii is expelled by cats when they shit and the cat shit is ingested by other creatures (consumption of unwashed vegetables, inhaled while digging close to the ground — which is why pregnant women are advised against gardening). T. gondii needs to get back into the digestive tract of a cat to reproduce, so it wriggles its way to the amygdale, the part of the brain responsible for emotional reaction, and causes the host to become attracted to cats, thus, in the case of small mammals or birds, becoming easy prey for cats (it is Carl Zimmer’s argument in his book, Parasite Rex that in this way parasites are like ecological catalysts, spinning food webs ever more tightly together).
But then there is the question of humans. It is one thing to say that T. gondii might make a bird or a rat suicidal. But T. gondii infects humans too. What then?
The scientific interviewee for the segment is Robert Sapolsky, a professor of neurology at Stanford University. On the question of T. gondii altering human behavior, he declares it highly plausible:
Sapolsky: Pure speculation, but people who think about this stuff view it as not purely speculative. The notion that toxo can produce some sort of attraction to cats in humans: they don’t think it’s all that crazy.
That’s right: crazy cat lady is that way because she’s been body-snatched by toxoplasma gondii.
Less controversial than the idea that T. gondii might be making crazy cat people out of us is the idea that it can make people more prone to engage in risky behavior. Dr. Sapolsky mentions two independent studies that show that people infected with T. gondii are two to six times more likely to get in a car crash than those not infected. With this information in hand, host and guest make the larger point:
Ellen Horne: It might be possible — might be possible — that toxo is guiding our emotions, changing who we are in some basic way. And if you consider that toxo might just be one of thousands of tiny little parasites inside us, pulling our strings from the inside, well that thought is pretty creepy.
Sapolsky: Even if the entire lesson with toxo is that a small subset of infected people now have one half of one percent more likelihood of wanting to drive really recklessly, even lurking in that one half of one percent are some serious implications for thinking about free will. We haven’t a clue the biology lurking in the background that makes free will seem a little bit suspect.
I’m less concerned with that old philosophical saw of free will versus determinism, than with extending an idea from segment on the hookworms. Mr. Lawrence says, “We function like rainforests; we’re ecosystems.” Presumably he is referring to our bodies. But the implication of toxoplasma gondii is that we are ecosystems in out minds as well. To the naïve sort of homunculus, Herman’s Head notion of consciousness, we must now add a few animal spirits.
Update, 23 October 2009: For instance this woman must have a pretty severe infection of T. gondii.
Update no. 2, 5 June 2010: Parasitogenic felinophilia (Toxoplasma gondii) may be treatable with haloperidol, an antipsychotic (“A Game of Cat and Mouse,” The Economist, 3 June 2010). Repost from my twitter feed.
The central idea of sociobiology is that the emergence of social creatures (herd animals) coincided with the creation of what might be termed a socio-cultural environment. The socio-cultural environment is as much an environment that social creatures inhabited as the material environment. As social creatures evolve, two things happen to the socio-cultural environment:
As with evolution of species morphology, the maximum complexity of socio-cultural environments increases (there is selection pressure on the entire socio-cultural environment as, say, predators develop way of thwarting or exploiting the social aspect of their prey and the social species evolve to countervail this development, e.g. parasitic cordyceps and ants; that is, there is species-level selection, since a social characteristic unrecognized by a counterpart comes to nothing; consider this as an analogy for fourth generation warfare).
Subsequent generations of herd animals come to rely ever more heavily upon social cohesion — as opposed to horns, honed perceptive apparatus, efficient digestion, et cetera — as their primary means of survival.
As this socio-cultural environment becomes more sophisticated and intricate and increasingly important as a means of survival, the socio-cultural environment grows in importance as the universe of factors shaping the evolution of social animals, while the objective, geological, hydrological and biological environment recedes in its evolutionary force.
Sexual selection (a type of sociobiological selection, as opposed to natural or Malthusian selection) is the sort of selection pressure that a species faces when its fellows, rather than the environment becomes the main challenge to getting its genes into the future. The shifting balance of natural selection and sexual selection in the play of evolutionary forces is meta-evolutionary. Evolution is recursive, with developments in the subjects of evolution backpropigating into the mechanism itself. In this respect every new thing in the universe (or at least in the effective realm) can potentially alter the functioning of the evolutionary dynamic. In this broadened perspective, the idea of machine or meme evolution supplanting biological evolution should not be so surprising.
Among a certain sector of the wildly technologically enthusiastic (among whom I count myself, though Matthew Crawford’s Shop Class as Soulcraft: An Inquiry Into the Value of Work is presently doing a lot to kick the piss out of this pretention), there is a notion that humans are rapidly disencumbering themselves of the material world and constructing for ourselves a world of pure ideas, information, mind-stuff. At some point in human history saber-toothed tigers, virulent microbes, droughts and tar pits ceased to be the primary challenge to humans seeking to survive and reproduce. Such extra-human threats were replaced as the primary danger by human-originating threats such as careening contraptions, shoddy construction techniques, insufficient precaution with the kitchen fire, marauding hoplites, jilted dagger-wielding lovers, corrupt institutions and flawed regimes of succession in governance. It is at the point where today it is plausible that the human socio-cultural environment has attained a level of preponderance where even the level of environmental catastrophe such as an asteroid strike that caused the mass extinctions of the past might be thwarted by the constituents of the human socio-cultural environment (on the other hand, the complexity of our socio-cultural environment might be just the sort of run-away biological factor that caused past mass extinction such as the oxygen catastrophe or the Canfield ocean thesis of the Permian–Triassic extinction event). In this conception, it is usually the the information revolution, the invention of the computer — a brain-like device — that is the cause of this transcending of matter. The advent of technology was not the key turning point. The recognition of sociobiology is that this trend is an aspect of evolution; that it long predates not only technology, but also even predates humans. In this way, we are not unique, not the penultimate branch of the tree of life, but only the latest in a succession of forms.
Update, 15 September 2009: It’s worth noting that while computers are not the revolution, nor the source of the revolution, they do form a paradigm, shaping our conceptualizations in ways that allow us to perceive the revolution.
Knowledge is a network phenomenon. Only primitive knowledge consists of non-systematized catalogues of facts. System is the highest state of knowledge. Right now the system of our knowledge might be said to be clumpy, with well developed disciplines, but tenuous connections between them. Knowledge is still subject to cluster analysis. The apogee of knowledge will be a system of complete propositional consistency.
I present here a selection of discussions of the network nature of knowledge:
Kevin Kelly (“The Fifth and Sixth Discontinuity,” The Technium, 15 June 2009):
We casually talk about the “discovery of America” in 1492, or the “discovery of gorillas” in 1856, or the “discovery of vaccines” in 1796. Yet vaccines, gorillas and America were not unknown before their “discovery.” Native peoples had been living in the Americas for 10,000 years before Columbus arrived and they had explored the continent far better than any European ever could. Certain West African tribes were intimately familiar the gorilla, and many more primate species yet to be “discovered.” Dairy farmers had long been aware of the protective power of vaccines that related diseases offered, although they did not have a name for it. The same argument can be made about whole libraries worth of knowledge — herbal wisdom, traditional practices, spiritual insights — that are “discovered” by the educated but only after having been long known by native and folk peoples. These supposed “discoveries” seems imperialistic and condescending, and often are.
Yet there is one legitimate way in which we can claim that Columbus discovered America, and the French-American explorer Paul du Chaillu discovered gorillas, and Edward Jenner discovered vaccines. They “discovered” previously locally known knowledge by adding it to the growing pool of structured global knowledge. Nowadays we would call that accumulating structured knowledge science. Until du Chaillu’s adventures in Gabon any knowledge about gorillas was extremely parochial; the local tribes’ vast natural knowledge about these primates was not integrated into all that science knew about all other animals. Information about “gorillas” remained outside of the structured known. In fact, until zoologists got their hands on Paul du Chaillu’s specimens, gorillas were scientifically considered to be a mythical creature similar to Big Foot, seen only by uneducated, gullible natives. Du Chaillu’s “discovery” was actually science’s discovery. The meager anatomical information contained in the killed animals was fitted into the vetted system of zoology. Once their existence was “known,” essential information about the gorilla’s behavior and natural history could be annexed. In the same way, local farmers’ knowledge about how cowpox could inoculate against small pox remained local knowledge and was not connected to the rest of what was known about medicine. The remedy therefore remained isolated. When Jenner “discovered” the effect, he took what was known locally, and linked its effect into to medical theory and all the little science knew of infection and germs. He did not so much “discover” vaccines as much as he “linked in” vaccines. Likewise America. Columbus’s encounter put America on the map of the globe, linking it to the rest of the known world, integrating its own inherent body of knowledge into the slowly accumulating, unified body of verified knowledge. Columbus joined two large continents of knowledge into a growing global consilience.
The reason science absorbs local knowledge and not the other way around is because science is a machine we have invented to connect information. It is built to integrate new knowledge with the web of the old. If a new insight is presented with too many “facts” that don’t fit into what is already known, then the new knowledge is rejected until those facts can be explained. A new theory does not need to have every unexpected detail explained (and rarely does) but it must be woven to some satisfaction into the established order. Every strand of conjecture, assumption, observation is subject to scrutiny, testing, skepticism and verification. Piece by piece consilience is built.
Pierre Bayard (How to Talk About Books You Haven’t Read [New York: Bloomsbury, 2007]):
As cultivated people know (and, to their misfortune, uncultivated people do not), culture is above all a matter of orientation. Being cultivated is a matter not of having read any book in particular, but of being able to find your bearings within books as a system, which requires you to know that they form a system and to be able to locate each element in relation to the others. …
Most statements about a book are not about the book itself, despite appearances, but about the larger set of books on which our culture depends at that moment. It is that set, which I shall henceforth refer to as the collective library, that truly matters, since it is our mastery of this collective library that is at stake in all discussions about books. But this mastery is a command of relations, not of any book in isolation …
The idea of overall perspective has implications for more than just situating a book within the collective library; it is equally relevant to the task of situating each passage within a book. (pgs. 10-11, 12, 14)
And I might add that it is not only passages within a book, but passages between books. Books, passages, paragraphs, et cetera are all stand-ins for or not-quite-there-yet stabs at the notion of memes. It is the relation of memes that is critical and books or passages therefrom are proxies or meme carriers. A book is a bundle of memes. And those memes bear a certain set of relations to all the other memes bundled in all the other books (or magazines, memos, blog posts, radio broadcasts, conversations, thoughts, or any of the other carriers of memes).
This brings us to the ur-theory of them all, W.V.O. Quine’s thumb-nail sketch epistemology from “Two Dogmas of Empiricism,” (The Philosophical Review vol. 60, 1951, pp. 20-43; Reprinted in From a Logical Point of View [Cambridge, Mass.: Harvard University Press, 1953; second, revised, edition 1961]):
The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. Reevaluation of some statements entails re-evaluation of others, because of their logical interconnections — the logical laws being in turn simply certain further statements of the system, certain further elements of the field. Having reevaluated one statement we must reevaluate some others, whether they be statements logically connected with the first or whether they be the statements of logical connections themselves. But the total field is so undetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to reevaluate in the light of any single contrary experience. No particular experiences are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole.
If this view is right, it is misleading to speak of the empirical content of an individual statement — especially if it be a statement at all remote from the experiential periphery of the field. Furthermore it becomes folly to seek a boundary between synthetic statements, which hold contingently on experience, and analytic statements which hold come what may. Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?
For vividness I have been speaking in terms of varying distances from a sensory periphery. Let me try now to clarify this notion without metaphor. Certain statements, though about physical objects and not sense experience, seem peculiarly germane to sense experience — and in a selective way: some statements to some experiences, others to others. Such statements, especially germane to particular experiences, I picture as near the periphery. But in this relation of “germaneness” I envisage nothing more than a loose association reflecting the relative likelihood, in practice, of our choosing one statement rather than another for revision in the event of recalcitrant experience. For example, we can imagine recalcitrant experiences to which we would surely be inclined to accommodate our system by reevaluating just the statement that there are brick houses on Elm Street, together with related statements on the same topic. We can imagine other recalcitrant experiences to which we would be inclined to accommodate our system by reevaluating just the statement that there are no centaurs, along with kindred statements. A recalcitrant experience can, I have already urged, be accommodated by any of various alternative reevaluations in various alternative quarters of the total system; but, in the cases which we are now imagining, our natural tendency to disturb the total system as little as possible would lead us to focus our revisions upon these specific statements concerning brick houses or centaurs. These statements are felt, therefore, to have a sharper empirical reference than highly theoretical statements of physics or logic or ontology. The latter statements may be thought of as relatively centrally located within the total network, meaning merely that little preferential connection with any particular sense data obtrudes itself.
As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries — not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. Let me interject that for my part I do, qua lay physicist, believe in physical objects and not in Homer’s gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.
Image from Bollen, Johan, Herbert Van de Sompel, Aric Hagberg, Luis Bettencourt, Ryan Chute, et al., “Clickstream Data Yields High-Resolution Maps of Science,” Public Library of Science One, vol. 4, no. 3, March 2009, e4803, doi:10.1371/journal.pone.0004803. See article for a larger version.
Here’s why Charles Mudede has become one of my most closely followed blogger-thinkers: because his project is my project (“The End of Internalism,” SLOG, The Stranger, 9 June 2009):
I’m quietly building a case for the importance of Hegel in an age that cares neither for him or his direct descendant, Marx. A part of the case will, one, link Hegel’s concept of geist and its movement in time (world history) with the idea of the evolution of noosphere in Pierre Teilhard de Chardin’s Phenomenon of Man; and, two, link Hegel’s idea of absolute spirit with the ideas expressed in Alva Noë’s new book Out of Our Heads: Why You Are Not Your Brain, and Other Lessons from the Biology of Consciousness — some of these ideas can be heard on the Brain Science Podcast.
I am very interested in using contemporary information economy concepts such as the noosphere or general systems theory to reconstruct the Hegelian system. I’m less sure where Mr. Mudede is going with the second part of this, but Out of Our Heads is on my list now.
I have previously commented on my love of the movie π (“The Supernovae in Your Coffee Cup,” 2 November 2008). It left me with two enduring images: mixing coffee and cream as an example of turbulence, previously discussed; and the branching of tree limbs as an example of fractal symmetry. I love winter for its exposure of this fabulous phenomena, innocuously right over our heads. I am always a little sad for the arrival of spring and the enshrouding of all these thought-provoking fractals in greenery.
The picture above is of my favorite tree in the neighborhood where I live. The degree to which the pattern of major arc over two-thirds of growth length followed by sharp break and lesser arc over remainder of growth length is repeated trunk to twig is amazing. Notice the arc of the trunk: unlike many trees which follow one rule for trunk and a separate rule for the branches, this tree follows a single rule throughout.
We think of a fractal as a recursive algorithm, a mathematical formula. But there’s no math in that tree. The recipe for that fractal is coded somewhere in the tree’s DNA. But the DNA contains no fractal. The DNA is a bunch of nucleotides that are transcribed by messenger RNA that code amino acids that assemble into proteins that form the structures of cells. The cells then split and differentiate in response to a complex of internal chemical signals and environmental stimuli to grow in a pattern that is the fractal.
One might say that there is a fractal somewhere in that tree, but there are so many transformation rules between nucleotide sequence and fractal growth pattern, that it is only in a manner of speaking. I am reminded of Wittgenstein’s discussion of what constitutes following a rule and going against it (Philosophical Investigations, trans. G. E. M. Anscombe [Malden, Mass.: Blackwell, 1953]):
198. “But how can a rule shew me what I have to do at this point? Whatever I do is, on some interpretation, in accord with the rule.” — That is not what we ought to say, but rather: any interpretation still hangs in the air along with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning.
“Then can whatever I do be brought into accord with the rule?” — Let me ask this: what has the expression of a rule — say a sign-post — got to do with my actions? What sort of connection is there here? — Well perhaps this one: I have been trained to react to this sign in a particular way, and now I so react to it.
But that is only to give the causal connection; to tell how it has come about that we now go by the sign-post; not what this going-by-the-sign really consists in. On the contrary; I have further indicated that a person goes by a sign-post only in so far as there exists a regular use of sign posts, a custom.
199. Is what we call “obeying a rule” something that it would be possible for only one man to do, and to do only once in his life? — This is of course a note on the grammar of the expression “to obey a rule.”
It is not possible that there should have been only one occasion on which someone obeyed a rule. It is not possible that there should have been only one occasion on which a report was made, an order given or understood; and so on. — To obey a rule, to make a report, to give an order, to play a game of chess, are customs (uses, institutions).
To understand a sentence means to understand a language. To understand a language means to be master of a technique.
200. It is, of course, imaginable that two people belonging to a tribe unacquainted with games should sit at a chess-board and go through the moves of a game of chess; and even with all the appropriate mental accompaniments. And if we were to see it we should say they were playing chess. But now imagine a game of chess translated according to certain rules into a series of actions which we do not ordinarily associate with a game — say into yells and stamping of feet. And now suppose those two people to yell and stamp instead of playing the form of chess that we are used to; and this in such a way that their procedure is translatable by suitable rules into a game of chess. Should we still be inclined to say that they were playing a game? What right would one have to say so?
201. This is our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule. The answer was: if everything can be made out to accord with the rule, then it can also be made out to conflict with it. And so there would be neither accord nor conflict here.
It can be seen that there is a misunderstanding here from the mere fact that in the course of our argument we gave one interpretation after another; as if each one contented us at least for a moment, until we thought of yet another standing behind it. What this shews is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call “obeying the rule” and “going against it” in actual cases.
Of course Wittgenstein is writing about social phenomena where custom and training are factors, but the undecidability of rules is the point here. Socially dogmatic, we are dismissive of blatant divergence from consensus. Less dogmatic — but not free of dogma — science resorts to the metaphysical-aesthetic notion of Ockham’s razor with which to cut through the myriad of rules that might potentially be made to accord with observed behavior. Is there really a fractal in the tree’s DNA? The fractal pattern of tree growth is but an interpretation of the tree’s DNA — an interpretation that would be different given a differing machinery of RNA transcription, amino acid assembly, protein expression, etc.
Consider nihilism as a system of negativity. Rather than no system or anti-system, or the standard sort of system of theorem built upon axiom, et cetera, it is a system of contradiction, where each principle is canceled out by another, every theory perfectly balanced by another opposing until there is nothing left, or that the web of confusion grows so tangled that one is driven to the nihilistic act, where one has nothing left but to obliterate and wipe away the whole lot of ideas. Now consider the following two passages from Dostoevsky’s Notes from the Underground:
… on coming home on one of the foulest nights in Petersburg, I used to realize intensely that again I had been guilty of some particularly dastardly action that day, and that once more it was no earthly use crying over spilt milk; and inwardly, secretly, I used to go on nagging myself, worrying myself, accusing myself, till at last the bitterness I felt turned into a sort of shameful, damnable sweetness and finally, into real, positive delight!
Well, let us now have a look at this mouse inaction. Let us suppose, for instance, that its feelings are hurt (and its feelings are almost always hurt), and that it also wants to avenge itself. There will perhaps be a greater accumulation of spite in it than in l’homme de la nature et de la vérité. A nasty, mean little desire to repay whoever has ofended it in his own coin stirs within it more nasty perhaps than in l’homme de la nature et de la vérité; for because of his inborn stupidity l’homme de la nature et de la vérité looks upon his revenge merely as a matter of justice whereas because of its intense sensibility the mouse denies that there is any question of justice here. At last we come to the business itself, to the act of revenge. The unhappy mouse has already succeeded in piling up — in the form of questions and doubts — a large number of dirty tricks in addition to its original dirty trick; it has accumulated such a large number of insoluble questions round every one question that it is drowned in a sort of deadly brew, a stinking puddle made up of doubts, its flurries of emotion, and lastly, the contempt with which the plain men of action cover it from head to foot while they stand solemnly round as judges and dictators and split their sides with laughter at it. Well, of course, all that is left for it to do is to dismiss it with a disdainful wave of its little paw and with a smile of simulated contempt, in which it does not believe itself, and to scurry back ingloriously into its hole.
After reading Notes from the Underground it is hard not to see Nietzsche as at least partially derivative. Nietzsche was reading Dostoevsky in the years 1886-1887, including Notes from the Underground. Nietzsche wrote On the Genealogy of Morals during 1887 and it is Dostoevsky’s narrator from Notes from the Underground who is the patient that Nietzsche has on he sofa in On the Genealogy of Morals. The difference is that while Nietzsche shares Dostoevsky’s diagnosis of the sickness of the West, Dostoevsky is nostalgic for Christianity and nationalism, whereas Nietzsche advocates an experimentalism and futurism of pressing boldly on.
It’s one thing to recognize that the properties of the component aren’t those of the composite. But on the positive side and in the interstitiary of this seemingly commonplace observation lies an entire world. The fallacy of composition is perhaps the first and the most important recognition on the way to systems science. Characteristics don’t scale in a straightforward or linear way and emergent properties, complex systems, adaptation and evolution, ecology, intelligence and society1 are all the positive side of the recognition of the fallacy of composition.
I mention the notion of an interstitiary between components and composites because this distinction is often thought of as discreet and binary. That is, people imagine components and composites and no intermediate states. This is because when people think about the fallacy of composition, they tend think of a machine-type example, or one of substance and form, e.g. just because an ingot of metal is pretty durable doesn’t mean that a precision machine made of metal parts is too. But emergence-type phenomenon are a unique kind of composition not captured in the machine analogy of component and composition.
A machine is made of heterogeneous parts and that is misleading here. Each part is relatively property-thin and by themselves are just a collection of odd shapes. It is only when completely assembled that the function of the whole is manifest. Structure is everything in the machine. Intermediate states between parts strewn on the table and complete assembly accomplish nothing. Minor deviations from proscribed structure accomplish nothing. And the whole is efficient: that is, it is specifically designed to minimize emergent or any other extraneous characteristics. Design and emergence are at odds here.2
Emergence, complex systems, et cetera come about from collections of more or less homogeneous corpuscles interacting in a largely unstructured way.3 The major difference here is that while the machine has no or few remarkable intermediary states, scale is all-important in systems phenomena, which tend to display differing and unique behavior at various scales. And where the machine is highly structure sensitive, complex systems tend to be robust in their various states.4
The key is that more is different (nearly the motto of the discipline).5 The common sense imagining, prior to the fallacy of composition, is that things scale in a linear way. More means more of the same. Then there is second order sophistication about scale. People add in the notion of a discontinuity. Things scale until they reach a certain threshold, at which point there is a discontinuity. More is different. But this is still a relatively binary conception with simply two sides of the discontinuity: one side of the discontinuity where the logic of linear growth prevails and the other where that of emergence or complexity prevails. There is a third order sophistication about scale where the binary view of second order thinking is still too simple; where the relationship between scale and properties is continuously variable.
As opposed to these simpler first and second order notions, continuously variable growth and development happen through many phases distinguished by differing logics or marked by different epiphenomena (something more like the imaginary graph above). As a system or network gains in members or in interactions, one set of behaviors becomes strained and unstable as it approaches the upper-bound threshold of the given logic. The threshold crossed, the previous logic gives way to a new logic. The pattern repeats, with the new logic holding for a period, but it too petering out in favor of a subsequent logic. And so on. Or perhaps there are tiers of controlling logics operative simultaneously. There may be meta-epi-phenomena as the various transitions admit a pattern of cycling logics or a second order logic to their or relations.6 No behavior or sequence is fundamental to systems, or the process of growth or to any particular phenomenon. We should dispense with the idea of a sin qua non behavior of systems in favor of a continuum of potentially many different behaviors as a system grows and changes.7
I will make a few examples to demonstrate the changing relation of prevailing logic and a system phenomena under growth.
Multiple logics. Consider that paradigmatic example of complexity: grains of sand falling onto a pile (a Bak-Tang-Wiesenfeld sandpile). As grains fall onto the pile, they tumble down the side, and come to a rest according to a standard distribution. Most come to a rest close to the drop point so the pile grows in height, but only a few roll all the way to the bottom so the base remains largely the same area resulting in the incline of the sides of the pile grow ever steeper. But there is a range of values for which the ratio of base to height is stable. When the pile reaches its upper bound of stability, the pile collapses. But it doesn’t collapse all the way to a layer of sand one grain thick. The collapse comes to a halt once the pile has reached the lower bound of the ratio of base to height (the lower bound being where the slope of the side of the pile is such that friction overcomes gravity and momentum). The pile recommences its growth in height. With a new, broader base having been established, it will achieve a greater height this time before reaching the critical threshold.
The pile doesn’t grow continuously until collapse though. It is constantly experiencing local collapse. The sand pile demonstrates scale symmetry in so far as there are slides of all sizes starting with a single grain previously stable coming lose and tumbling a little further down a side. Single grains frequently start a chain reaction leading to larger slides. The collapse of the whole pile isn’t an phenomenon of it’s own, unrelated to the logic of local slides, as the catastrophic collapse of the pile is usually the result of a local slide running away to the scale of the entire pile.
But fractal collapse isn’t a constant. Rather, its probability is a function of where the pile is in the growth-collapse cycle. At the lower bound of the range of stability any collapse is almost impossible. A single grain may break lose and tumble to a more stable location, but owing to the widespread state of stability, it is not likely to set off a chain reaction leading to a large slide. At the top end, catastrophic collapse approaches certainty. A growing proportion of sand grains are in unstable positions. More are likely to break lose and, having broken lose, collide with other unstable grains setting off chain reactions. As the pile goes through the positive phase of the growth-collapse cycle, it traverses a range of increasing collapse probability from almost impossible to almost certain and its fractal dimension grows.
Tally the sheer number of logics at work in this seemingly unnoteworthy phenomenon. The overall pattern is linear growth — the pile grows in mass in equal units in equal time. The shape of the pile demonstrates an oscillating pattern, between a steep cone and a shallow cone. The height of the pile superficially demonstrates cyclical growth. Upon closer inspection, the growth of the height of the pile turns out to be fractal. But even that fractal growth isn’t constant, but one of increasing fractal dimension.
A complicated interstitiary. A discontinuity is probably always preceded by some sort of turbulence, a breakdown in the previously prevailing relationship. A prevailing logic doesn’t yield instantaneously to its successor. In at least materials science this is well documented in the form of the microstructure of phase transitions.
As a social scientific example, nuclear weapons represent a discontinuity in the growth of military power, but how much of one? Countries had already acquired “city-busting” and potentially civilization destroying capability using the regular old Newtonian technologies of modern air power and chemical explosives. The U.S. imagined “bombing Vietnam back to the stone age” employing conventional methods. So it would seem that military power (technology) had already crossed an inflection point and gone non-linear in a way that was necessitating major strategic reconsideration prior to the discontinuity of nuclear weapons.
Many discontinuities. People have a tendency to conceptualize consciousness in the model of the binary discontinuity. Neural networks grow in size from tiny nerve bundles in nematode worms up to pre-hominids and then somewhere in the Pleistocene whamo, the discontinuity and consciousness and that’s the pinnacle. Some people imagine the difference between regular people and geniuses to be a little discontinuity, rather than a difference of quantity. Hence the obsession with Einstein’s brain, Descartes’s skull, and so on.
But I imagine consciousness rather than a big bang being a development with perhaps a number of discontinuities and plateaus — the first reflex, the first pain, the first internal world model, the first declarative memory, the first language of discrete symbols, the first syntax, the first theory of mind — on the way to humans. But our intelligence is just another plateau on the path. There is the singularity somewhere beyond us and still more discontinuities, unimaginable to us even beyond that. As intelligence is not one thing, I imagine each of the many faculties having its own trajectory, each with multiple discontinuities of their own, as well as the synergy of the many faculties being of uneven development and their interplay subject to system effects.8
Instead of relying on the sort of intuitionism that says something like “We know that there has been a discontinuity in strategic thought because we read Thomas Schelling now instead of Helmuth von Moltke” we should dispenses with this intuitionistic approach in favor of systematic mathematical methods to analyze change — to determine when and where system effects are at work, which ones are at work, the extent of their range, the exact location of inflection points or discontinuities, where the logic of a tipping point takes over and the pace of accelerating assertion of the logic of the new régime, to study turbulence, islands of stability, equilibria, feedback and other patterns that can develop.9
I am prone to write “collective intelligence” in place of “society,” but an ancillary point here is that all intelligence is collective (composite), whether it’s a society, so to speak, of individually dumb neurons in the brain of an individual or the more commonplace idea of a society, namely wisdom of crowds, invisible hand, social networking, superorganism type phenomena.
Though not necessarily so: we are learning how to harness emergent properties to our purposes, to design them in.
Though structure might be a concomitant emergent property, e.g. ecologies might exist in equilibrium, but that’s not because competition among species is well ordered.
This category error of misconstruing different component-composition behavior types, or not even identifying the second type at all, is perhaps illuminating to the overarching issue of intelligent design’s constant irreducible complexity mongering. One of the favorite analogies from their rhetoric is that of the mousetrap: remove a single component and it isn’t a slightly less effective mousetrap, it isn’t an anything and natural selection can’t function on constellations that display no function. But notice how this relies entirely on the machine type of component-composition thinking. But if one sees phenotypic expression as an emergent property of genotypic change, than one might shift to the later version of the component-composition model. A heavily determined trait will be stable over many changes in the underlying genes, until a critical threshold is reached at which time rapid change in phenotype (the emergent property) could occur. A perfect example of the contrast between the two types of thinking that I am describing here is that version of evolution as the long, slow accumulation of mutation down through the millennia, which sees a more or less consistent, linear change, versus something like punctuated equilibrium which imagines different logics of change predominating under different circumstances. I would go further to say that punctuated equilibrium is only a theory of discontinuity. A more elaborate theory of the deep history dynamics of evolution, or a marcotheory of evolution, as opposed to the microtheory we have at present, is required.
More is not binary, though more is frequently discrete — neural networks grow in whole neurons, societies grow in whole people. But not always. System happens as much in analog as in digital phenomena, e.g. strategy must adapt as power or capability increase, but power does not grow in discrete units.
Meta-epi-phenomena would be something observable only over extremely long timeframes for most phenomena with which we are familiar. Kondratiev cycles (45-60 years) and Forrester waves (200 years) would be examples from economics and sociology. The existence of such long patterns, whose period is outside the scope of our limited record, is part of the explanation for black swan type phenomena. I imagine that there are small models, probably in physics and biology, where the dynamcs of such systems could be worked out in detail, then recognized in longer term examples based on partial data. As the patterns of systems theory are largely substratum independent, patterns discovered in one area are relevant to another. A well organized sub-discipline would better allow for the abstraction of higher-order patterns from their original fields of discovery and facilitate interdisciplinary transmission of knowledge. A pattern well characterized in observations of one phenomenon might be revolutionary to another area where the phenomenon is insufficiently well observed to know the entire continuum of behavior, but observed well enough to recognize that it is an instance of the former pattern. Systems-type phenomena are present throughout the various sciences. Just as mathematics is used throughout the sciences, but is consolidated into a discipline of its own, so too systems science should become a better organized and consolidated sub-discipline. As it involves such a diverse range of the sciences, it would be an interdisciplinary field, not one as autonomous as mathematics.
While none fundamental, there are, presumably, a finite set of possible system patterns. I wrote on the possibility of cataloguing and organizing them on some sort of periodic table of logics in “Formal Cognition,” 1 January 2008.
Animals have developed a variety of different types and levels of intelligence; there’s no reason to think that machine intelligence will be any different.
The problem is that the data sets that we have aren’t big enough, granular enough and are riddled with bad data. With two points you can’t tell linear from geometric growth. With three points you can’t tell geometric growth from linear growth with noise. And of course it gets much worse than this. And we don’t even know how to operationalize a large segment of the really interesting phenomena. How would we quantify something as elusive as national power — something international relations theorists are trying to do all the time — when even the component statistics are a mess?