Fitness landscapes

At Home in the Universe: The Search for the Laws of Self-Organization and Complexity (Kindle Edition)

Stuart Kauffman (Wikipedia)

• An American medical doctor, theoretical biologist, and complex systems researcher who studies the origin of life on Earth. He was a professor at the University of Chicago, University of Pennsylvania, and University of Calgary. He is currently emeritus professor of biochemistry at the University of Pennsylvania and affiliate faculty at the Institute for Systems Biology. He is best known for arguing that the complexity of biological systems and organisms might result as much from self-organization and far-from-equilibrium dynamics as from Darwinian natural selection as discussed in his book Origins of Order (1993). 

Quick takeaway:

• The book’s central thesis is that complexity in general (and life in particular) is an inevitable consequence of self organizing principles that come into play with non-equilibrium systems. He explores the underlying principles in a variety of ways including binary networks, autocatalytic sets, NK models, and fitness landscapes, both static and co-evolving.
• When I was reading this 20 year old book, I had the impression that his work, particularly on how fitness landscapes are explored have direct relevance to the construction of complex systems today. In particular I was struck by how applicable his work with fitness landscapes and NK models would be to the evaluation of the hyperparameter space associated with building Neural Networks.
• Another point that I found particularly compelling is his descriptions of the incalculable size of the high-dimension spaces of combinatorial possibility. The number of potential combinations on even a smallish binary network would take more time in than the universe has to calculate. As such, there need to be mechanisms that allow for a faster, “good enough” evaluation of the space. That’s why we have historical narratives. They describe a path through this space that has worked. As an example, compare tic-tac-toe to chess. In the former, the every possibility in the game space can be known. Chess has too many possibilities, so instead there are openings, gambits, and endgames, discovered by chess masters that come to us as stories.

Notes:

• Chapter 1: At home in the Universe
  • In all these cases, the order that emerges depends on robust and typical properties of the systems, not on the details of structure and function. Under a vast range of different conditions, the order can barely help but express itself. (page 19)
  • Nonequilibrium ordered systems like the Great Red Spot are sustained by the persistent dissipation of matter and energy, and so were named dissipative structures by the Nobel laureate Ilya Prigogine some decades ago. These systems have received enormous attention. In part, the interest lies in their contrast to equilibrium thermodynamic systems, where equilibrium is associated with collapse to the most probable, least ordered states. In dissipative systems, the flux of matter and energy through the system is a driving force generating order. In part, the interest lies in the awareness that free-living systems are dissipative structures, complex metabolic whirlpools. (page 21).
  • The theory of computation is replete with deep theorems. Among the most beautiful are those showing that, in most cases by far, there exists no shorter means to predict what an algorithm will do than to simply execute it, observing the succession of actions and states as they unfold. The algorithm itself is its own shortest description. It is, in the jargon of the field, incompressible. (page 22)
  • And yet, even if it is true that evolution is such an incompressible process, it does not follow that we may not find deep and beautiful laws governing that unpredictable flow. For we are not precluded from the possibility that many features of organisms and their evolution are profoundly robust and insensitive to details. (page 23)
  • Strikingly, such coevolving systems also behave in an ordered regime, a chaotic regime, and a transition regime. (page 27)
    • Note that this reflects our Nomadic (chaotic), Flocking (transition) and Stampeding (ordered) states
  • This seemingly haphazard process also shows an ordered regime where poor compromises are found quickly, a chaotic regime where no compromise is ever settled on, and a phase transition where compromises are achieved, but not quickly. The best compromises appear to occur at the phase transition between order and chaos. (page 28)
• Chapter 4: Order for Free
  • But evolution requires more than simply the ability to change, to undergo heritable variation. To engage in the Darwinian saga, a living system must first be able to strike an internal compromise between malleability and stability. To survive in a variable environment, it must be stable, to be sure, but not so stable that it remains forever static. Nor can it be so unstable that the slightest internal chemical fluctuation causes the whole teetering structure to collapse. (page 73)
  • To survive in a variable environment, it must be stable, to be sure, but not so stable that it remains forever static. Nor can it be so unstable that the slightest internal chemical fluctuation causes the whole teetering structure to collapse. (pg 73)
  • It is now well known that in most cells, such molecular feedback can give rise to complex chemical oscillations in time and space. (page 74)
    • Olfati-Saber and graph laplacians!
  • The point in using idealizations in science is that they help capture the main issues. Later one must show that the issues so captured are not altered by removing the idealizations. (page 75)
    • Start with observation, build initial simulation and then measure the difference and modify
  • If started in one state, over time the system will flow through some sequence of states. This sequence is called a trajectory (page 77)
    • I wonder if this can be portrayed as a map? You have to go through one state to get to the next. In autocatalytic systems there may be multiple systems that may be similar and yet have branch points (plant cells, animal cells, bacteria)
  • To answer these questions we need to understand the concept of an attractor. More than one trajectory can flow into the same state cycle. Start a network with any of these different initial patterns and, after churning through a sequence of states, it will settle into the same state cycle, the same pattern of blinking. In the language of dynamical systems, the state cycle is an attractor and the collection of trajectories that flow into it is called the basin of attraction. We can roughly think of an attractor as a lake, and the basin of attraction as the water drainage flowing into that lake. (page 78)
    • Also applicable to social and socio-technical systems. The technology changes the connectivity which could change the shape of the landscape
  • One feature is simply how many “inputs” control any lightbulb. If each bulb is controlled by only one or two other lightbulbs, if the network is “sparsely connected,” then the system exhibits stunning order. If each bulb is controlled by many other light-bulbs, then the network is chaotic. So “tuning” the connectivity of a network tunes whether one finds order or chaos. The second feature that controls the emergence of order or chaos is simple biases in the control rules themselves. Some control rules, the AND and OR Boolean functions we talked about, tend to create orderly dynamics. Other control rules create chaos. (page 80)
    • In our more velocity-oriented system, this is Social Influence Horizon) and is dynamic over time
  • Consider networks in which each lightbulb receives input from only one other. In these K = 1 networks, nothing very interesting happens. They quickly fall into very short state cycles, so short that they often consist of but a single state, a single pattern of illumination. Launch such a K = 1 network and it freezes up, saying the same thing over and over for all time. (page 81)
  • At the other end of the scale, consider networks in which K = N, meaning that each lightbulb receives an input from all lightbulbs, including itself. One quickly discovers that the length of the networks’ state cycles is the square root of the number of states. Consider the implications. For a network with only 200 binary variables—bulbs that can be on or off—there are 2200 or 1060 possible states. (page 81)
  • Such K = N networks do show signs of order, however. The number of attractors in a network, the number of lakes, is only N/e, where e is the basis of the natural logarithms, 2.71828. So a K = N network with 100,000 binary variables would harbor about 37,000 of these attractors. Of course, 37,000 is a big number, but very very much smaller than 2100,000, the size of its state space. (page 82)
    • Need to look into if there is some kind of equivalent in the SIH settings
  • The order arises, sudden and stunning, in K = 2 networks. For these well-behaved networks, the length of state cycles is not the square root of the number of states, but, roughly, the square root of the number of binary variables. Let’s pause to translate this as clearly as we can. Think of a randomly constructed Boolean network with N = 100,000 lightbulbs, each receiving K = 2 inputs. The “wiring diagram” would look like a madhatterly scrambled jumble, an impenetrable jungle. Each lightbulb has also been assigned at random a Boolean function. The logic is, therefore, a similar mad scramble, haphazardly assembled, mere junk. The system has 2100,000 or 1030,000 states—megaparsecs of possibilities—and what happens? The massive network quickly and meekly settles down and cycles among the square root of 100,000 states, a mere 317. (page 83)
  • The reason complex systems exist on, or in the ordered regime near, the edge of chaos is because evolution takes them there. (page 89)
• Chapter 5: The Mystery of Ontology
  • Another way to ensure orderly behavior is to construct networks using what are called canalyzing Boolean functions. These Boolean rules have the easy property that at least one of the molecular inputs has one value, which might be 1 or 0, which by itself can completely determine the response of the regulated gene. The OR function is an example of a canalyzing function (Figure 5.3a). An element regulated by this function is active at the next moment if its first, or its second, or both inputs are active at the current moment. Thus if the first input is active, then the regulated element is guaranteed to be active at the next moment, regardless of the activity of the second input. (page 103)
    • This is max pooling
  • For most perturbations, a genomic system on any attractor will exhibit homeostatic return to the same attractor. The cell types are fundamentally stable. But for some perturbations, the system flows to a different attractor. So differentiation occurs naturally. And the further critical property is this: from any one attractor, it is possible to undergo transitions to only a few neighboring attractors, and from them other perturbations drive the system to still other attractors. Each lake, as it were, is close to only a few other lakes. (page 110)
• Chapter 6: Noah’s Vessel
  • That we eat our meals rather than fusing with them marks, I believe, a profound fact. The biosphere itself is supracritical. Our cells are just subcritical. Were we to fuse with the salad, the molecular diversity this fusion would engender within our cells would unleash a cataclysmic supracritical explosion. The explosion of molecular novelty would soon be lethal to the unhappy cells harboring the explosion. The fact that we eat is not an accident, one of many conceivable methods evolution might have alighted on to get new molecules into our metabolic webs. Eating and digestion, I suspect, reflect our need to protect ourselves from the supracritical molecular diversity of the biosphere. (page 122)
  • We may be discovering a universal in biology, a new law: if our cells are subcritical, then, presumably, so too are all cells—bacteria, bracken, fern, bird, man. Throughout the supracritical explosion of the biosphere, cells since the Paleozoic, cells since the start, cells since 3.45 billion years ago must have remained subcritical. If so, then this subcritical–supracritical boundary must have always set an upper limit on the molecular diversity that can be housed within one cell. A limit exists, then, on the molecular complexity of the cell. (page 126)
  • If local ecosystems are metabolically poised at the subcritical–supracritical boundary, while the biosphere as a whole is supracritical? Then what a new tale we tell, of life cooperating to beget ever new kinds of molecules, and a biosphere where local ecosystems are poised at the boundary, but have collectively crept slowly upward in total diversity by the supracritical character of the whole planet. The whole biosphere is broadly collectively autocatalytic, catalyzing its own maintenance and ongoing molecular exploration. (page 130)
• Chapter 8: High-Country Adventures
  • what would happen if, in addition to attempting to evolve such a computer program, we were more ambitious and attempted to evolve the shortest possible program that will carry out the task? Such a “shortest program” is one that is maximally compressed; that is, all redundancies have been squeezed out of it. Evolving a serial computer program is either very hard or essentially impossible because it is incredibly fragile. Serial computer programs contain instructions such as “compare two numbers and do such and such depending on which is larger” or “repeat the following action 1,000 times.” The computation performed is extremely sensitive to the order in which actions are carried out, the precise details of the logic, numbers of iterations, and so forth. The result is that almost any random change in a computer program produces “garbage.” Familiar computer programs are precisely the kind of complex systems that do not have the property that small changes in structure yield small changes in behavior. Almost all small changes in structure lead to catastrophic changes in behavior. (page 152)
    • This is the inherent problem we are grappling with in our “barely controlled systems”. All the elements involved are brittle and un-evolvable
  • It seems likely that there is no way to evolve a maximally compressed program in less time than it would take to exhaustively generate all possible programs, testing each to see if it carries out the desired task. When all redundancy has been squeezed from a program, virtually any change in any symbol would be expected to cause catastrophic variation in the behavior of the algorithm. Thus nearby variants in the program compute very different algorithms. (page 154)
  • because the program is maximally compressed, any change will cause catastrophic alterations in the computation performed. The fitness landscape is entirely random. The next fact is this: the landscape has only a few peaks that actually perform the desired algorithm. In fact, it has recently been shown by the mathematician Gregory Chaitin that for most problems there is only one or, at most, a few such minimal programs. It is intuitively clear that if the landscape is random, providing no clues about good directions to search, then at best the search must be a random or systematic search of all the 10300 possible programs to find the needle in the haystack, the possibly unique minimal program. This is just like finding Mont Blanc by searching every square meter of the Alps; the search time is, at best, proportional to the size of the program space. (page 155)
    • I’ve been thinking about hyperparameter tuning in the wrong way. There need(?) to be two approaches – one that works in evolvable spaces where there can be gradualism. The other approach cas to work in discontinuous regions, such as what activation function to use.
  • The question of what kinds of complex systems can be assembled by an evolutionary search process not only is important for understanding biology, but may be of practical importance in understanding technological and cultural evolution as well. The sensitivity of our most complex artifacts to catastrophic failure from tiny causes—for example, the Challenger disaster, the failed Mars Observer mission, and power-grid failures affecting large regions—suggests that we are now butting our heads against a problem that life has nuzzled for enormously longer periods: how to produce complex systems that do not teeter on the brink of collapse. Perhaps general principles governing search in vast spaces of possibilities cover all these diverse evolutionary processes, and will help us design—or even evolve—more robust systems. (page 157)
  • Once we understand the nature of these random landscapes and evolution on them, we will better appreciate what it is about organisms that is different, how their landscapes are nonrandom, and how that nonrandomness is critical to the evolutionary assembly of complex organisms. We will find reasons to believe that it is not natural selection alone that shapes the biosphere. Evolution requires landscapes that are not random. The deepest source of such landscapes may be the kind of principles of self-organization that we seek. (page 165)
  • On random landscapes, finding the global peak by searching uphill is totally useless; we have to search the entire space of possibilities. But even for modestly complex genotypes, or programs, that would take longer than the history of the universe. (page 167)
  • Things capable of evolving—metabolic webs of molecules, single cells, multicellular organisms, ecosystems, economic systems, people—all live and evolve on landscapes that themselves have a special property: they allow evolution to “work.” These real fitness landscapes, the types that underlie Darwin’s gradualism, are “correlated.” Nearby points tend to have similar heights. The high points are easier to find, for the terrain offers clues about the best directions in which to proceed. (page 169)
  • In short, the contribution to overall fitness of the organism of one state of one trait may depend in very complex ways on the states of many other traits. Similar issues arise if we think of a haploid genotype with N genes, each having two alleles. The fitness contribution of one allele of one gene to the whole organism may depend in complex ways on the alleles of other genes. Geneticists call this coupling between genes epistasis or epistatic coupling, meaning that genes at other places on the chromosomes affect the fitness contribution of a gene at a given place. (page 170)
  • The NK model captures such networks of epistatic couplings and models the complexity of the coupling effects. It models epistasis itself by assigning to each trait, or gene, epistatic “inputs” from K other traits or genes. Thus the fitness contribution of each gene depends on the gene’s own allele state, plus the allele states of the K other genes that affect that gene. (page 171)
  • I find the NK model fascinating because of this essential point: altering the number of epistatic inputs per gene, K, alters the ruggedness and number of peaks on the landscape. Altering K is like twisting a control knob. (page 172)
    •  This is really important and should also work with graph laplacians. In other words, not only can we model the connectivity, we can model the stiffness
  • our model organism, with its network of epistatic interactions among its genes, is caught in a web of conflicting constraints. The higher K is—the more interconnected the genes are—the more conflicting constraints exist, so the landscape becomes ever more rugged with ever more local peaks. (page 173)
    • This sounds oddly like how word2vec is calculated. Which implies that all connected neural networks are correlated and epistatic.
  • It is these conflicting constraints that make the landscape rugged and multipeaked. Because so many constraints are in conflict, there is a large number of rather modest compromise solutions rather than an obvious superb solution. (page 173)
    • Dimension reduction and polarization are a social solution to this problem
  • landscapes with moderate degrees of ruggedness share a striking feature: it is the highest peaks that can be scaled from the greatest number of initial positions! This is very encouraging, for it may help explain why evolutionary search does so well on this kind of landscape. On a rugged (but not random) landscape, an adaptive walk is more likely to climb to a high peak than a low one. If an adapting population were to “jump” randomly into such a landscape many times and climb uphill each time to a peak, we would find that there is a relationship between how high the peak is and how often the population climbed to it. If we turned our landscapes upside down and sought instead the lowest valleys, we would find that the deepest valleys drain the widest basins. (page 177)
  • The property that the highest peaks are the ones to which the largest fraction of genotypes can climb is not inevitable. The highest peaks could be very narrow but very high pinnacles on a low-lying landscape with modest broad hilltops. If an adapting population were released at a random spot and walked uphill, it would then find itself trapped on the top of a mere local hilltop. The exciting fact we have just discovered is that for an enormous family of rugged landscapes, the NK family, the highest peaks “drain” the largest basins. This may well be a very general property of most rugged landscapes reflecting complex webs of conflicting constraints. (page 177)
    •  I think this may be a function of how the landscapes are made. The K in NK somewhat dictates the amount of correlation
  • Recall another striking feature of random landscapes: with every step one takes uphill, the number of directions leading higher is cut by a constant fraction, one-half, so it becomes ever harder to keep improving. As it turns out, the same property shows up on almost any modestly rugged or very rugged landscape. Figure 8.9 shows the dwindling fraction of fitter neighbors along adaptive walks for different K values (Figure 8.9a) and the increased waiting times to find fitter variants for different K values (Figure 8.9b). Once K is modestly large, about K = 8 or greater, at each step uphill the number of directions uphill falls by a constant fraction, and the waiting time or number of tries to find that way uphill increases by a constant fraction. This means that as one climbs higher and higher, it becomes not just harder, but exponentially harder to find further directions uphill. So if one can make one try per unit time, the rate of improving slows exponentially. (page 178)
    • This is very important in understanding how hyperparameter space needs to be explored
  • Optimal solutions to one part of the overall design problem conflict with optimal solutions to other parts of the overall design. Then we must find compromise solutions to the joint problem that meet the conflicting constraints of the different subproblems. (page 179)
  • Selection, in crafting the kinds of organisms that exist, may also help craft the kinds of landscapes over which they evolve, picking landscapes that are most capable of supporting evolution—not only by mutation alone, but by recombination as well. Evolvability itself is a triumph. To benefit from mutation, recombination, and natural selection, a population must evolve on rugged but “well-correlated” landscapes. In the framework of NK landscapes, the “K knob” must be well tuned. (page 182)
    • This is going to be the trick for machine learning
  • even if the population is released on a local peak, it may not stay there! Simply put, the rate of mutation is so high that it causes the population to “diffuse” away from the peak faster than the selective differences between less fit and more fit mutants can return the population to the peak. An error catastrophe, first discovered by Nobel laureate Manfred Eigen and theoretical chemist Peter Schuster, has occurred, for the useful genetic information built up in the population is lost as the population diffuses away from the peak. (page 184)
  • Eigen and Schuster were the first to emphasize the importance of this error catastrophe, for it implies a limit to the power of natural selection. At a high enough mutation rate, an adapting population cannot assemble useful genetic variants into a working whole; instead, the mutation-induced “diffusion” over the space overcomes selection, pulling the population toward adaptive peaks. (page 184)
  • This limitation is even more marked when seen from another vantage point. Eigen and Schuster also emphasized that for a constant mutation rate per gene, the error catastrophe will arise when the number of genes in the genotype increases beyond a critical number. Thus there appears to be a limit on the complexity of a genome that can be assembled by mutation and selection! (page 184)
  • We are seeking a new conceptual framework that does not yet exist. Nowhere in science have we an adequate way to state and study the interleaving of self-organization, selection, chance, and design. We have no adequate framework for the place of law in a historical science and the place of history in a lawful science. (page 185)
    • This is the research part of the discussion in the iConference paper. Use the themes in the following paragraphs (self organization, selection, etc. ) to build up the areas that need to be discussed and researched.
  • The inevitability of historical accident is the third theme. We can have a rational morphology of crystals, because the number of space groups that atoms in a crystal can occupy is rather limited. We can have a periodic table of the elements because the number of stable arrangements of the subatomic constituents is relatively limited. But once at the level of chemistry, the space of possible molecules is vaster than the number of atoms in the universe. Once this is true, it is evident that the actual molecules in the biosphere are a tiny fraction of the space of the possible. Almost certainly, then, the molecules we see are to some extent the results of historical accidents in this history of life. History arises when the space of possibilities is too large by far for the actual to exhaust the possible. (page 186)
  • Here is a firm foothold: an evolutionary process, to be successful, requires that the landscapes it searches are more or less correlated. (page 186)
    • This is a meta design constraint that needs to be discussed (iConference? Antonio’s workshop?)
  • Nonequilibrium systems can be robust as well. A whirlpool dissipative system is robust in the sense that a wide variety of shapes of the container, flow rates, kinds of fluids, and initial conditions of the fluids lead to vortices that may persist for long periods. So small changes in the construction parameters of the system, and initial conditions, lead to small changes in behavior. (page 187)
  • Whirlpools are attractors in a dynamical system. Attractors, however, can be both stable and unstable. Instability arises in two senses. First, small changes in the construction of the system may dramatically alter the behavior of the system. Such systems are called structurally unstable. In addition, small changes in initial conditions, the butterfly effect, can sharply change subsequent behavior. Conversely, stable dynamical systems can be stable in both senses. Small changes in construction may typically lead to small changes in behavior. The system is structurally stable. And small changes in initial conditions can lead to small changes in behavior. (page 187)
  • We know that there is a clear link between the stability of the dynamical system and the ruggedness of the landscape over which it adapts. Chaotic Boolean networks, and many other classes of chaotic dynamical systems, are structurally unstable. Small changes wreak havoc on their behavior. Such systems adapt on very rugged landscapes. In contrast, Boolean networks in the ordered regime are only slightly modified by mutations to their structure. These networks adapt on relatively smooth fitness landscapes. (page 187)
  • We know from the NK landscape models discussed in this chapter that there is a relationship between the richness of conflicting constraints in a system and the ruggedness of the landscape over which it must evolve. We plausibly believe that selection can alter organisms and their components so as to modify the structure of the fitness landscapes over which those organisms evolve. By taking genomic networks from the chaotic to the ordered regime, selection tunes network behavior to be sure. By tuning epistatic coupling of genes, selection also tunes landscape structure from rugged to smooth. Changing the level of conflicting constraints in the construction of an organism from low to high tunes how rugged a landscape such organisms explore. (page 188)
  • And so we return to a tantalizing possibility: that self-organization is a prerequisite for evolvability, that it generates the kinds of structures that can benefit from natural selection. It generates structures that can evolve gradually, that are robust, for there is an inevitable relationship among spontaneous order, robustness, redundancy, gradualism, and correlated landscapes. Systems with redundancy have the property that many mutations cause no or only slight modifications in behavior. Redundancy yields gradualism. But another name for redundancy is robustness. Robust properties are ones that are insensitive to many detailed alterations. The robustness of the lipid vesicle, or of the cell type attractors in genomic networks in the ordered regime, is just another version of redundancy. Robustness is precisely what allows such systems to be molded by gradual accumulation of variations. Thus another name for redundancy is structural stability—a folded protein, an assembled virus, a Boolean network in the ordered regime. The stable structures and behaviors are ones that can be molded. (page 188)
    • This is why evolution may be the best approach for machine learning hyperparameter tuning
  • If this view is roughly correct, then precisely that which is self-organized and robust is what we are likely to see preeminently utilized by selection. (page 188)
  • The more rare and improbable the forms that selection seeks, the less typical and robust they are and the stronger will be the pressure of mutations to revert to what is typical and robust. (page 189)
• Chapter 9: Organisms and Artifacts
  •  Might the same general laws govern major aspects of biological and technological evolution? Both organisms and artifacts confront conflicting design constraints. As shown, it is those constraints that create rugged fitness landscapes. Evolution explores its landscapes without the benefit of intention. We explore the landscapes of technological opportunity with intention, under the selective pressure of market forces. But if the underlying design problems result in similar rugged landscapes of conflicting constraints, it would not be astonishing if the same laws governed both biological and technological evolution. (page 192)
  • I begin by describing a simple, idealized kind of adaptive walk—long-jump adaptation—on a correlated but rugged landscape. We have already looked at adaptive walks that proceed by generating and selecting single mutations that lead to fitter variants. Here, an adaptive walk proceeds step-by-step in the space of possibilities, marching steadfastly uphill to a local peak. Suppose instead that we consider simultaneously making a large number of mutations that alter many features at once, so that the organism takes a “long jump” across its fitness landscape. Suppose we are in the Alps and take a single normal step. Typically, the altitude where we land is closely correlated with the altitude from which we started. There are, of course, catastrophic exceptions; cliffs do occur here and there. But suppose we jump 50 kilometers away. The altitude at which we land is essentially uncorrelated with the altitude from which we began, because we have jumped beyond what is called the correlation length of the landscape. (page 192)
  • A very simple law governs such long-jump adaptation. The result, exactly mimicking adaptive walks via fitter single-mutant variants on random landscapes is this: every time one finds a fitter long-jump variant, the expected number of tries to find a still better long-jump variant doubles! (page 193)
    • Intelligence is computation, and expensive
  • As the number of genes increases, long-jump adaptations becomes less and less fruitful; the more complex an organism, the more difficult it is to make and accumulate useful drastic changes through natural selection. (Page 194)
  • The germane issue is this: the “universal law” governing long-jump adaptation suggests that adaptation on a correlated landscape should show three time scales—an observation that may bear on the Cambrian explosion. Suppose that we are adapting on a correlated, but rugged NK landscape, and begin evolving at an average fitness value. Since the initial position is of average fitness, half of all nearby variants will be better. But because of the correlation structure or shape of the landscape, those nearby variants are only slightly better. In contrast, consider distant variants. Because the initial point is of average fitness, again half the distant variants are fitter. But because the distant variants are far beyond the correlation length of the landscape, some of them can be very much fitter than the initial point. (By the same token, some distant variants can be very much worse.) Now consider an adaptive process in which some mutant variants change only a few genes, and hence search the nearby vicinity, while other variants mutate many genes, and hence search far away. Suppose that the fittest of the variants will tend to sweep through the population the fastest. Thus early in such an adaptive process, we might expect the distant variants, which are very much fitter than the nearby variants, to dominate the process. If the adapting population can branch in more than one direction, this should give rise to a branching process in which distant variants of the initial genotype, differing in many ways from one another as well, emerge rapidly. Thus early on, dramatically variant forms should arise from the initial stem. Just as in the Cambrian explosion, the species exhibiting the different major body plans, or phyla, are the first to appear. (Page 195)
  • Because the fraction of fitter nearby variants dwindles very much more slowly than in the long-jump case. In short, in the mid term of the process, the adaptive branching populations should begin to climb local hills. (Page 195)
  • The implication is this: when fitness is average, the fittest variants will be found far away. As fitness improves, the fittest variants will be found closer and closer to the current position. (Page 196)
    • So with hyperparameter tuning, change many variables initially, and reduce as the fitness results level out and proceed up the local hill
  • Uniting these two features of rugged but correlated landscapes, we should find radiation that initially both is bushy and occurs among dramatically different variants, and then quiets to scant branching among similar variants later on as fitness increases. (page 198)
  • Despite the fact that human crafting of artifacts is guided by intent and intelligence, both processes often confront problems of conflicting constraints. (Page 202)
    • Dimension reduction is a way of reducing those constraints, but the cost is ignoring the environment. Ideologies must be simple to allow for dense connection without conflict
  • As better designs are found, it becomes progressively harder to find further improvements, so variations become progressively more modest. Insofar as this is true, it is obviously reminiscent of the claims for the Cambrian explosion, where the higher taxa filled in from the top down. (Page 202)
    • This is a design trap. Since designing for more constraints limits hill climbing, designing for individuals and cultures could make everything grind to a halt. Designing for cultures needs to have a light footprint
  • There is something very familiar about this in the context of technological trajectories and learning effects: the rate of finding fitter variants (that is, making better products or producing them more cheaply) slows exponentially, and then ceases when a local optimum is found. This is already almost a restatement of two of the well-known aspects of learning effects. First, the total number of “tries” between finding fitter variants increases exponentially; thus we expect that increasingly long periods will pass with no improvements at all, and then rapid improvements as a fitter variant is suddenly found. Second, adaptive walks that are restricted to search the local neighborhood ultimately terminate on local optima. Further improvement ceases. (Page 204)
  • it seems worthwhile to consider seriously the possibility that the patterns of branching radiation in biological and technological evolution are governed by similar general laws. Not so surprising, this, for all these forms of adaptive evolution are exploring vast spaces of possibilities on more or less rugged “fitness” or “cost” landscapes. If the structures of such landscapes are broadly similar, the branching adaptive processes on them should also be similar. (Page 205)
• Chapter 10: An Hour upon the Stage
  • The vast puzzle is that the emergent order in communities—in community assembly itself, in coevolution, and in the evolution of coevolution—almost certainly reflects selection acting at the level of the individual organism. (Page 208)
  • Models like those of Lotka and Volterra have provided ecologists with simple “laws” that may govern predator-prey relationships. Similar models study the population changes, or population dynamics, when species are linked into more complex communities with tens, hundreds, or thousands of species. Some of these links are “food webs,” which show which species eat which species. But communities are more complex than food webs, for two species may be mutualists, may be competitors, may be host and parasite, or may be coupled by a variety of other linkages. In general, the diverse populations in such model communities might exhibit simple steady-state patterns of behavior, complex oscillations, or chaotic behavior. (Page 211)
    • Building an ecology for intelligent machines means doing this. I guess we’ll find out what it’s like to build the garden of eden
  • Pimm and his colleagues have struggled to understand these phenomena and have arrived at ideas deeply similar to the models of fitness landscapes we discussed in Chapter 8 and 9. Different communities are imagined as points on a community landscape. Change the initial set of species, and the community will climb to a different peak, a different stable community. (Page 212)
  • In these models, Pimm and friends toss randomly chosen species into a “plot” and watch the population trajectories. If any species goes to zero population, hence extinct, it is “removed” from the plot. The results are both fascinating and still poorly understood. What one finds is that, at first, it is easy to add new species, but as more species are introduced, it becomes harder and harder. That is, more randomly chosen species must be tossed into the plot to find one that can survive with the rest of the assembling community. Eventually, the model community is saturated and stable; no further species can be added. (Page 212)
  • The community-assembly simulation studies are fascinating for a number of reasons beyond the distribution of extinction events. In particular, it is not obvious why model communities should “saturate,” so that it becomes increasingly difficult and finally impossible to add new species. If one constructs a “community landscape,” in which each point of the terrain represents a different combination of species, then the peaks will represent points of high fitness—combinations that are stable. While a species navigates a fitness landscape by mutating genes, a community navigates a community landscape by adding or deleting a species. Pimm argues that as communities climb higher and higher toward some fitness peak, the ascension becomes harder and harder. As the climb proceeds, there are fewer directions uphill, and hence it is harder to add new species. At a peak, no new species can be added. Saturation is attained. And from one initial point the community can climb to different local peaks, each representing a different stable community. (Page 214)
    • In belief spaces, this could help to explain the concept of velocity. It is mechanism for stumbling into new parts of the fitness landscape. And there is something about how ideas go stale.
  • In a coevolutionary arms race, when the Red Queen dominates, all species keep changing and changing their genotypes indefinitely in a never-ending race merely to sustain their fitness level. (Page 216)
    • This should also apply to belief spaces
  • Two main behaviors are imagined. The first image is of Red Queen behavior, where all organisms keep changing their genotypes in a persistent “arms race,” and hence the coevolving population never settles down to an unchanging mixture of genotypes. The second main image is of coevolving populations within or between species that reach a stable ratio of genotypes, an evolutionary stable strategy, and then stop altering genotypes. Red Queen behavior is, as we will soon see, a kind of chaotic behavior. ESS behavior, when all species stop changing, is a kind of ordered regime. (Page 221)
  • Just as we can use the NK model to show how genes interact with genes or how traits interact with traits within one organism, we can also use it to show how traits interact with traits between organisms in an ecosystem. (Page 225)
  • The ecosystem tends to settle into the ordered, evolutionary stable strategies regime if either epistatic connections, K, within each species are high, so that there are lots of peaks to become trapped on, or if couplings between species, C, is low, so landscapes do not deform much at the adaptive moves of the partners. Or an ESS regime might result when a third parameter, S, the number of species each species interacts with, is low, so that moves by one do not deform the landscapes of many others. (Page 226)
  • There is also a chaotic Red Queen regime where the species virtually never stop coevolving (Figure 10.4c). This Red Queen regime tends to occur when landscapes have few peaks to get trapped on, thus when K is low; when each landscape is deformed a great deal by adaptive moves of other species, thus when C is high; or when S is high so that each species is directly affected by very many other species. Basically, in this case, each species is chasing peaks that move away faster than the species can chase them. (Page 228)
  • At first, it might seem surprising that low K leads to chaotic ecosystems; in the NK Boolean networks, high K led to chaos. The more inter-couplings, the more likely a small change was to propagate throughout and cause the Boolean system to veer off into butterfly behavior. But with coupled landscapes it is the interconnectedness between the species that counts. When intercoupling, C, is high, moves by one species strongly deform the fitness landscapes of its partners. If any trait in the frog is affected by many traits in the fly, and vice versa, then a small change in traits of one species alters the landscape of the other a lot. The system will tend to be chaotic. Conversely, the ecosystem will tend to be in the ordered regime when the couplings between species, C, is sufficiently low. For much the same reason, if we were to keep K and C the same, but change the number of species S any one species directly interacts with, we would find that if the number is low the system will tend to be ordered, while if the number is high the ecosystem will tend to be chaotic. (Page 228)
    • There is something about Tajfel’s opposition identity that might lead to Red Queen scenarios. This would also help to explain the differences between left and right wing behaviours. Right wing is driven by “liberal tears” more than the opposition.
  • In fact, the results of our simulations suggest that the very highest fitness occurs precisely between ordered and chaotic behavior! (Page 228)
  • 
  • Tuning an ecosystem. As the richness of epistatic connections between species, K, is increased, tuning the ecosystem from the chaotic to the orderly regime, average fitness at first increases and then decreases. It reaches the highest value midway between the extremes. The experiment is based on a 5 × 5 square lattice ecosystem, in which each of 25 species interacts with at most four other species. (Species on the corners of the lattice interact with two neighbors [CON = 2]; species on the edges interact with three neighbors [CON = 3]; and interior species interact with four neighbors [CON = 4]. N = 24, C = 1, S =25.) (page 229)
  • One might start the system with all species having very high K values, coevolving on very rugged landscapes, or all might have very low K values, coevolving on smooth landscapes. If K were not allowed to change, then deep within the high-K ordered regime, species would settle to ESS rapidly; that is, species would climb to poor local peaks and cling to them. In the second, low K, Red Queen chaotic regime, species would never attain fitness peaks. The story no longer stops there, however, for the species can now evolve the ruggedness of their landscapes, and the persistent attempts by species to invade new niches, when successful, will insert a new species into an old niche and may disrupt any ESS attained. (Page 232)
  • 
  • Figures 10.7 and 10.8 show these results. Each species has N = 44 traits; hence epistatic coupling can be as high as 43, creating random landscapes, or as low as 0, creating Fujiyama landscapes. As generations pass, the average value of K in the coevolving system converges onto an intermediate value of K, 15 to 25, and stays largely within this narrow range of intermediate landscape ruggedness (Above)). Here fitness is high, and the species do reach ESS equilibria where all genotypes stop changing for considerable periods of time, before some invader or invaders disrupt the balance by driving one or more of the coadapted species extinct. (Page 232)
  • When K is held high or low, deep in the ordered regime or deep in the chaotic regime, huge extinction avalanches rumble through the model ecosystems. The vast sizes of these events reflect the fact that fitness is low deep in the ordered regime because of the high-K conflicting constraints, and fitness is low deep in the chaotic regime because of the chaotic rising and plunging fitness values. In either case, low fitness of a species makes it very vulnerable to invasion and extinction. The very interesting result is that when the coevolving system can adjust its K range, it self-tunes to values where average fitness is as high as possible; therefore, the species are least vulnerable to invasion and extinction, so extinction avalanches appear to be as rare as possible. This shows up in Figure 10.8, which compares the size distribution and total number of extinction events deep in the ordered regime and after the system has self-tuned to optimize landscape ruggedness, K, and fitness. After the ecosystem self-tunes, the avalanches of extinction events remain a power law—the slope is about the same as when deep in the ordered regime. But over the same total number of generations, far fewer extinction events of each size occur. The self-tuned ecosystem also has far fewer extinction events than does an ecosystem deep in the chaotic regime. In short, the ecosystem self-tunes to minimize the rate of extinction! As if by an invisible hand, all the coevolving species appear to alter the rugged structures of the landscapes over which they evolve such that, on average, all have the highest fitness and survive as long as possible. (Page 234)
• Chapter 11: In Search of Excellence
  • Organisms, artifacts, and organizations all evolve and coevolve on rugged, deforming, fitness landscapes. Organisms, artifacts, and organizations, when complex, all face conflicting constraints. So it can be no surprise if attempts to evolve toward good compromise solutions and designs must seek peaks on rugged landscapes. Nor, since the space of possibilities is typically vast, can it be a surprise that even human agents must search more or less blindly. Chess, after all, is a finite game, yet no grand master can sit at the board after two moves and concede defeat because the ultimate checkmate by the opponent 130 moves later can now be seen as inevitable. And chess is simple compared with most of real life. We may have our intentions, but we remain blind watchmakers. We are all, cells and CEOs, rather blindly climbing deforming fitness landscapes. If so, then the problems confronted by an organization—cellular, organismic, business, governmental, or otherwise—living in niches created by other organizations, is preeminently how to evolve on its deforming landscape, to track the moving peaks. (Page 247)
  • Evolution is a search procedure on rugged fixed or deforming landscapes. No search procedure can guarantee locating the global peak in an NP-hard problem in less time than that required to search the entire space of possibilities. And that, as we have repeatedly seen, can be hyperastronomical. Real cells, organisms, ecosystems, and, I suspect, real complex artifacts and real organizations never find the global optima of their fixed or deforming landscapes. The real task is to search out the excellent peaks and track them as the landscape deforms. Our “patches” logic appears to be one way complex systems and organizations can accomplish this. (Page 248)
  • The basic idea of the patch procedure is simple: take a hard, conflict-laden task in which many parts interact, and divide it into a quilt of nonoverlapping patches. Try to optimize within each patch. As this occurs, the couplings between parts in two patches across patch boundaries will mean that finding a “good” solution in one patch will change the problem to be solved by the parts in the adjacent patches. Since changes in each patch will alter the problems confronted by the neighboring patches, and the adaptive moves by those patches in turn will alter the problem faced by yet other patches, the system is just like our model coevolving ecosystems. Each patch is the analogue of what we called a species in Chapter 10. Each patch climbs toward fitness peaks on its own landscape, but in doing so deforms the fitness landscapes of its partners. As we saw, this process may spin out of control in Red Queen chaotic behavior and never converge on any good overall solution. Here, in this chaotic regime, our system is a crazy quilt of ceaseless changes. Alternatively, in the analogue of the evolutionary stable strategy (ESS) ordered regime, our system might freeze up, getting stuck on poor local peaks. Ecosystems, we saw, attained the highest average fitness if poised between Red Queen chaos and ESS order. We are about to see that if the entire conflict-laden task is broken into the properly chosen patches, the coevolving system lies at a phase transition between order and chaos and rapidly finds very good solutions. Patches, in short, may be a fundamental process we have evolved in our social systems, and perhaps elsewhere, to solve very hard problems. (Page 253)
  • It is the very fact that patches coevolve with one another that begins to hint at powerful advantages of patches compared with the Stalinist limit of a single large patch. What if, in the Stalinist limit, the entire lattice settles into a “bad” local minimum, one with high energy rather than an excellent low-energy minimum? The single-patch Stalinist system is stuck forever in the bad minimum. Now let’s think a bit. If we break the lattice up into four 5 × 5 patches just after the Stalinist system hits this bad minimum, what is the chance that this bad minimum is not only a local minimum for the lattice as a whole, but also a local minimum for each of the four 5 × 5 patches individually? You see, in order for the system broken into four patches to “stay” at the same bad minimum, it would have to be the case that the same minimum of the entire lattice happens also to be a minimum for all four of the 5 × 5 patches individually. If not, one or more of the patches will be able to flip a part, and hence begin to move. Once one patch begins to move, the entire lattice is no longer frozen in the bad local minimum. (Page 256)
  • Breaking large systems into patches allows the patches literally to coevolve with one another. Each climbs toward its fitness peaks, or energy minima, but its moves deform the fitness landscape or energy landscape of neighboring patches. (Page 257)
  • In the chaotic Leftist Italian limit, the average energy achieved by the lattice is only a slight bit less, about 0.47. In short, if the patches are too numerous and too small, the total system is in a disordered, chaotic regime. Parts keep flipping between their states, and the average energy of the lattice is high. (Page 258)
  • The answer depends on how rugged the landscape is. Our results suggest that if K is low so the landscape is highly correlated and quite smooth, the best results are found in the Stalinist limit. For simple problems with few conflicting constraints, there are few local minima in which to get trapped. But as the landscape becomes more rugged, reflecting the fact that the underlying number of conflicting constraints is becoming more severe, it appears best to break the total system into a number of patches such that the system is near the phase transition between order and chaos. (Page 258)
  • Here, then, is the first main and new result. It is by no means obvious that the lowest total energy of the lattice will be achieved if the lattice is broken into quilt patches, each of which tries to lower its own energy regardless of the effects on surrounding patches. Yet this is true. It can be a very good idea, if a problem is complex and full of conflicting constraints, to break it into patches, and let each patch try to optimize, such that all patches coevolve with one another. (Page 262)
  • But what, if anything, characterizes the optimum patch-size distribution? The edge of chaos. Small patches lead to chaos; large patches freeze into poor compromises. When an intermediate optimum patch size exists, it is typically very close to a transition between the ordered and the chaotic regime. (Page 262)
    • I’m pretty sure that this can be determined iteratively and within a desired epsilon. It should resemble the way a neural net converges on an accuracy.
  • I find it fascinating that hard problems with many linked variables and loads of conflicting constraints can be well solved by breaking the entire problem into nonoverlapping domains. Further, it is fascinating that as the conflicting constraints become worse, patches become ever more helpful. (Page 264)
  • I suspect that analogues of patches, systems having various kinds of local autonomy, may be a fundamental mechanism underlying adaptive evolution in ecosystems, economic systems, and cultural systems. (Page 254)
  • We are constructing global communication networks, and whipping off into space in fancy tin cans powered by Newton’s third law. The Challenger disaster, brownouts, the Hubble trouble, the hazards of failure in vast linked computer networks—our design marvels press against complexity boundaries we do not understand. (Page 265)
  • Patching systems so that they are poised on the edge of chaos may be extremely useful for two quite different reasons: not only do such systems rapidly attain good compromise solutions, but even more essentially, such poised systems should track the moving peaks on a changing landscape very well. The poised, edge-of-chaos systems are “nearly melted.” Suppose that the total landscape changes because external conditions alter. Then the detailed locations of local peaks will shift. A rigid system deep in the ordered regime will tend to cling stubbornly to its peaks. Poised systems should track shifting peaks more fluidly. (Page 266)
  • Misspecification arises all the time. Physicists and biologists, trying to figure out how complex biopolymers such as proteins fold their linear sequence of amino acids into compact three-dimensional structures, build models of the landscape guiding such folding and solve for the deep energy minima. Having done so, the scientists find that the real protein does not look like the predicted one. The physicists and biologists have “guessed” the wrong potential surface; they have guessed the wrong landscape and hence have solved the wrong hard problem. They are not fools, for we do not know the right problem. (Page 266)
    • Same for Hyperparameter tuning
  • We must learn how to learn in the face of persistent misspecification. Suppose we model the production facility, and learn from that model that a particular way to break it into patches is optimal, allowing the system to converge on a suggested solution. If we have misspecified the problem, the detailed solution is probably of little value. But it may often be the case that the optimal way to break the problem into patches is itself very insensitive to misspecifications of the problem. In the NK lattice and patch model we have studied, a slight change in the NK landscape energies will shift the locations of the minima substantially, but may not alter the fact that the lattice should still be broken into 6 × 6 patches. Therefore, rather than taking the suggested solution to the misspecified problem and imposing it on the real facility, it might be far smarter to take the suggested optimal patching of the misspecified problem, impose that on the real production facility, and then try to optimize performance within each of the now well-defined patches. In short, learning how to optimize the misspecified problem may not give us the solution to the real problem, but may teach us how learn about the real problem, how to break it into quilt patches that coevolve to find excellent solutions. (Page 267)
    • This is really worth looking at, because it can apply to round tripping simulation and real world systems as well. And a fitness test could be the time to divergence
  • receiver-based communication is roughly this: all the agents in a system that is trying to coordinate behavior let other agents know what is happening to them. The receivers of this information use it to decide what they are going to do. The receivers base their decisions on some overall specification of “team” goal. (Page 268)
  • 
  • This observation suggests that it might be useful if, in our receiver-based communication system, we allowed sites to ignore some of their customers. Let’s say that each site pays attention to itself and a fraction, P, of its customers, and ignores 1 – P of them. What happens if we “tune” P? What happens is shown in Figure 11.8. The lowest energy for the entire lattice occurs when a small fraction of customers is ignored! As Figure 11.8 shows, if each site tries to help itself and all its customers, the system does less well than if each site pays attention, on average, to about 95 percent of its customers. In the actual numerical simulation, we do this by having each site consider each of its customers and pay attention to that customer with a 95 percent probability. In the limit where each site pays attention to no customers, of course, energy of the entire lattice is very high, and hence bad. (Page 268)
• Chapter 12: An Emerging Global Civilization
  • Catalytic closure is not mysterious. But it is not a property of any single molecule; it is a property of a system of molecules. It is an emergent property. (Page 275)
  • But Fontana found a second type of reproduction. If he “disallowed” general copiers, so they did not arise and take over the soup, he found that he evolved precisely what I might have hoped for: collectively autocatalytic sets of Lisp expressions. That is, he found that his soup evolved to contain a “core metabolism” of Lisp expressions, each of which was formed as the product of the actions of one or more other Lisp expressions in the soup. (Page 278)
  • Fontana called copiers “level-0 organizations” and autocatalytic sets “level-1 organizations (Page 279)
  • The ever-transforming economy begins to sound like the ever-transforming biosphere, with trilobites dominating for a long, long run on Main Street Earth, replaced by other arthropods, then others again. If the patterns of the Cambrian explosion, filling in the higher taxa from the top down, bespeak the same patterns in early stages of a technological trajectory when many strong variants of an innovation are tried until a few dominant designs are chosen and the others go extinct, might it also be the case that the panorama of species evolution and coevolution, ever transforming, has its mirror in technological coevolution as well? Maybe principles deeper than DNA and gearboxes underlie biological and technological coevolution, principles about the kinds of complex things that can be assembled by a search process, and principles about the autocatalytic creation of niches that invite the innovations, which in turn create yet further niches. It would not be exceedingly strange were such general principles to exist. Organismic evolution and coevolution and technological evolution and coevolution are rather similar processes of niche creation and combinatorial optimization. While the nuts-and-bolts mechanisms underlying biological and technological evolution are obviously different, the tasks and resultant macroscopic features may be deeply similar. (Page 281)
  • The difficulty derives from the fact that economists have no obvious way to build a theory that incorporates what they call complementarities. The automobile and gasoline are consumption complementarities. You need both the car and the gas to go anywhere. (Page 282)
    • I think that graph laplacians might provide some insight into this behavior
      • Graph laplacian dissertation
  • The use, I claim, is that we can discover the kinds of things that we would expect in the real world if our “as if” mock-up of the true laws lies in the same universality class. Physicists roll out this term, “universality class,” to refer to a class of models all of which exhibit the same robust behavior. So the behavior in question does not depend on the details of the model. Thus a variety of somewhat incorrect models of the real world may still succeed in telling us how the real world works, as long as the real world and the models lie in the same universality class. (Page 283)
    • Universality classes in nonequilibrium lattice systems
  • An “enzyme” might be a symbol string in the same pot with a “template matching” (000) site somewhere in it. Here the “enzyme match rule” is that a 0 on the enzyme matches a 1 on the substrate, rather like nucleotide base-pairing. Then given such a rule for “enzymatic sites,” we can allow the symbol strings in the pot to act on one another. One way is to imagine two randomly chosen symbol strings colliding. If either string has an “enzymatic site” that matches a “substrate site” on the other, then the enzymatic site “acts on” the substrate site and carries out the substitution mandated in the corresponding row (Page 285)
  • Before we turn to economic models, let us consider some of the kinds of things that can happen in our pot of symbol strings as they act on one another, according to the laws of substitution we might happen to choose. A new world of possibilities lights up and may afford us clues about technological and other forms of evolution. Bear in mind that we can consider our strings as models of molecules, models of goods and services in an economy, perhaps even models of cultural memes such as fashions, roles, and ideas. Bear in mind that grammar models give us, for the first time, kinds of general “mathematical” or formal theories in which to study what sorts of patterns emerge when “entities” can be both the “object” acted on and transformed and the entities that do the acting, creating niches for one another in their unfolding. Grammar models, therefore, help make evident patterns we know about intuitively but cannot talk about very precisely. (Page 287)
  • These grammar models also suggest a possible new factor in economic takeoff: diversity probably begets diversity; hence diversity may help beget growth. (Page 292)
    •  

      Diversity begets growth opportunities. Pure growth is fastest in a monoculture of simple items with short maturity cycles

  • The number of renewable goods with which an economy is endowed is plotted against the number of pairs of symbol strings in the grammar, which captures the hypothetical “laws of substitutability and complementarity.” A curve separates a subcritical regime below the curve and a supracritical regime above the curve. As the diversity of renewable resources or the complexity of the grammar rules increases, the system explodes with a diversity of products. (Page 193)
  • Friend, you cannot even predict the motions of three coupled pendula. You have hardly a prayer with three mutually gravitating objects. We let loose pesticides on our crops; the insects become ill and are eaten by birds that sicken and die, allowing the insects to proliferate in increased abundance. The crops are destroyed. So much for control. Bacon, you were brilliant, but the world is more complex than your philosophy. (Page 302)

Hanna Arendt – Thinking Without a Banister

These two connected statements had already been torn asunder by a tradition that translated the one by declaring that man is a social being, a banality for which one would not have needed Aristotle, and the other by defining man as the animal rationale, the reasoning animal. (pg 23)

What Aristotle had seen as one and the same human quality, to live together with others in the modus of speaking, now became two distinct characteristics, to have reason and to be social. And these two characteristics, almost from the beginning, were not thought merely to be distinct, but antagonistic to each other: the conflict between man’s rationality and his sociability can be seen throughout our tradition of political thought (pg 23)

The law was now no longer the boundary (which the citizens ought to defend like the walls of the city, because it had the same function for the citizens’ political life as the city’s wall had for their physical existence and distinctness, as Heraclitus had said), but became a yardstick by which rule could be measured. Rule now either conformed to or overruled the law, and in the latter case the rule was called tyrannical usually, although not necessarily, exerted by one man-and therefore a kind of perverted monarchy. From then on, law and power became the two conceptual pillars of all definitions of government, and these definitions hardly changed during the more than two thousand years that separate Aristotle from Montesquieu. (pg 28)

But bureaucracy should not be mistaken for totalitarian domination. If the October Revolution had been permitted to follow the lines prescribed by Marx and Lenin, which was not the case, it would probably have resulted in bureaucratic rule. The rule of nobody, not anarchy, or disappearance of rule, or oppression, is the ever present danger of any society based on universal equality. (pg 33)

In Marx’s own opinion, what made socialism scientific and distinguished it from that of his predecessors, the “utopian socialists,” was not an economic theory with its scientific insights as well as its errors, but the discovery of a law of movement that ruled matter and, at the same time, showed itself in the reasoning capacity of man as “consciousness,” either of the self or of a class. (pg 35)

The logic of dialectal movement enables Marx to combine nature with history, or matter with man; man becomes the author of a meaningful, comprehensible history because his metabolism with nature, unlike an animal’s, is not merely consumptive but requires an activity, namely, labor. For Marx labor is the uniting link between matter and man, between nature and history. He is a “materialist” insofar as the specifically human form of consuming matter is to him the beginning of everything (pg 35)

Politics, in other words, is derivative in a twofold sense: it has its origin in the pre-political data of biological life, and it has its end in the post-political, highest possibility of human destiny (pg 40)

the fact that the multitude, whom the Greeks called hoi polloi, threatens the existence of every single person, runs like a red thread throughout the centuries that separate Plato from the modern age. In this context it is irrelevant whether this attitude expresses itself in secular terms, as in Plato and Aristotle, or if it does so in the terms of Christianity. (pg 40)

true Christians wohnen fern voneinander, that is, dwell far from each other and are as forlorn among the multitude as were the ancient philosophers. (pg 41)

Each new birth endangers the continuity of the polis because with each new birth a new world potentially comes into being. The laws hedge in these new beginnings and guarantee the preexistence of a common world, the permanence of a a continuity that transcends the individual life span of e each generation, and in which each single man in his mortality can hope to leave a trace of permanence behind him. (pg 46)

introduced the terms nomo and physei, by law or by nature. Thus, the order of the universe, the kosmos of natural things, was differentiated from the world of human affairs, whose order is laid down by men since it is an order of things made and done by men This distinction too, survives in the beginning of our tradition, where Aristotle expressly States that political science deals with things that are nomo and not physei. (pg 47)

Beyond Individual Choice: Teams and Frames in Game Theory

• Michael Bacharach
• Natalie Gold
• Robert Sugden
• From Amazon.com: In the classical tradition of game theory, Bacharach models human beings as rational actors, but he revises the standard definition of rationality to incorporate two major new ideas. He enlarges the model of a game so that it includes the ways agents describe to themselves (or “frame”) their decision problems. And he allows the possibility that people reason as members of groups (or “teams”), each taking herself to have reason to perform her component of the combination of actions that best achieves the group’s common goal. Bacharach shows that certain tendencies for individuals to engage in team reasoning are consistent with recent findings in social psychology and evolutionary biology.
• The following list of notes is oldest (bottom) to newest (top)
• It is a central component of resolute choice, as presented by McClennen, that (unless new information becomes available) later transient agents recognise the authority of plans made by earlier agents. Being resolute just is recognising that authority (although McClennen’ s arguments for the rationality and psychological feasibility of resoluteness apply only in cases in which the earlier agents’ plans further the common ends of earlier and later agents). This feature of resolute choice is similar to Bacharach’ s analysis of direction, explained in section 5. If the relationship between transient agents is modelled as a sequential game, resolute choice can be thought of as a form of direction, in which the first transient agent plays the role of director; the plan chosen by that agent can be thought of as a message sent by the director to the other agents. To the extent that each later agent is confident that this plan is in the best interests of the continuing person, that confidence derives from the belief that the first agent identified with the person and that she was sufficiently rational and informed to judge which sequence of actions would best serve the person’s objectives. (pg 197)
• The problem posed by Heads and Tails is not that the players lack a common understanding of salience; it is that game theory lacks an adequate explanation of how salience affects the decisions of rational players. All we gain by adding preplay communication to the model is the realisation that game theory also lacks an adequate explanation of how costless messages affect the decisions of rational players. (pg 180)
• The fundamental principle of this morality is that what each agent ought to do is to co-operate, with whoever else is co-operating, in the production of the best consequences possible given the behaviour of non-co-operators’ (Regan 1980, p. 124). (pg 167)
• Ordered On Social Facts
  • Are social groups real in any sense that is independent of the thoughts, actions, and beliefs of the individuals making up the group? Using methods of philosophy to examine such longstanding sociological questions, Margaret Gilbert gives a general characterization of the core phenomena at issue in the domain of human social life.
• Schema 3: Team reasoning (from a group viewpoint) pg 153
  • We are the members of S.
  • Each of us identifies with S.
  • Each of us wants the value of U to be maximized.
  • A uniquely maximizes U.
  • Each of us should choose her component of A.
• Schema 4: Team reasoning (from an individual viewpoint) pg 159
  • I am a member of S.
  • It is common knowledge in S that each member of S identifies
    with S.
  • It is common knowledge in S that each member of S wants the
    value of U to be maximized.
  • It is common knowledge in S that A uniquely maximizes U.
  • I should choose my component of A.
• Schema 7: Basic team reasoning pg 161
  • I am a member of S.
  • It is common knowledge in S that each member of S identifies
    with S.
  • It is common knowledge in S that each member of S wants the
    value of U to be maximized.
  • It is common knowledge in S that each member of S knows his
    component of the profile that uniquely maximizes U.
  • I should choose my component of the profile that uniquely
    maximizes U.
    • Bacharach notes to himself the ‘hunch’ that this schema is ‘the basic rational capacity’ which leads to high in Hi-Lo, and that it ‘seems to be indispensable if a group is ever to choose the best plan in the most ordinary organizational circumstances’. Notice that Schema 7 does not require that the individual who uses it know everyone’s component of the profile that maximizes U.
• His hypothesis is that group identification is an individual’s psychological response to the stimulus of a particular decision situation. It is not in itself a group action. (To treat it as a group action would, in Bacharach’ s framework, lead to an infinite regress.) In the theory of circumspect team reasoning, the parameter w is interpreted as a property of a psychological mechanism-the probability that a person who confronts the relevant stimulus will respond by framing the situation as a problem ‘for us’. The idea is that, in coming to frame the situation as a problem ‘for us’, an individual also gains some sense of how likely it is that another individual would frame it in the same way; in this way, the value of w becomes common knowledge among those who use this frame. (Compare the case of the large cube in the game of Large and Small Cubes, discussed in section 4 of the introduction.) Given this model, it seems that the ‘us’ in terms of which the problem is framed must be determined by how the decision situation first appears to each individual. Thus, except in the special case in which w == 1, we must distinguish S (the group with which individuals are liable to identify, given the nature of the decision situation) from T (the set of individuals who in fact identify with S). pg 163
• The psychology of group identity allows us to understand that group identification can be due to factors that have nothing to do with the individual preferences. Strong interdependence and other forms of common individual interest are one sort of favouring condition, but there are many others, such as comembership of some existing social group, sharing a birthday, and the artificial categories of the minimal group paradigm. (pg 150)
• Wherever we may expect group identity we may also expect team reasoning. The effect of team reasoning on behavior is different from that of individualistic reasoning. We have already seen this for Hi-Lo. This has wide implications. It makes the theory of team reasoning a much more powerful explanatory and predictive theory than it would be if it came on line only in games with th3e right kind of common interest. To take just one example, if management brings it about so that the firm’s employees identify with the firm, we may expect for them to team-reason and so to make choices that are not predicted by the standard theories of rational choice.(pg 150)
• As we have seen, the same person passes through many group identities in the flux of life, and even on a single occasion more than one of these identities may be stimulated. So we will need a model of identity in which the probability of a person’s identification is distributed over not just two alternatives-personal self-identity or identity with a fixed group-but, in principle, arbitrarily many. (pg 151)
• The explanatory potential of team reasoning is not confined to pure coordination games like Hi-Lo. Team reasoning is assuredly important for its role in explaining the mystery facts about Hi-Lo; but I think we have stumbled on something bigger than a new theory of behaviour in pure coordination games. The key to endogenous group identification is not identity of interest but common interest giving rise to strong interdependence. There is common interest in Stag Hunts, Battles of the Sexes, bargaining games and even Prisoner’s Dilemmas. Indeed, in any interaction modelable as a ‘mixed motive’ game there is an element of common interest. Moreover, in most of the landmark cases, including the Prisoner’s Dilemma, the common interest is of the kind that creates strong interdependence, and so on the account of chapter 2 creates pressure for group identification. And given group identification, we should expect team reasoning.(pg 144)
• There is a second evolutionary argument in favour of the spontaneous team-reasoning hypothesis. Suppose there are two alternative mental mechanisms that, given common interest, would lead humans to act to further that interest. Other things being equal, the cognitively cheapest reliable mechanism will be favoured by selection. As Sober and Wilson (1998) put it, mechanisms will be selected that score well on availability, reliability and energy efficiency. Team reasoning meets these criteria; more exactly, it does better on them than the alternative heuristics suggested in the game theory and psychology literature for the efficient solution of common-interest games. (pg 146)
•  (pg 149)
• I think MB is getting at the theory for why there is explore/exploit in populations
• We have progressed towards a plausible explanation of the behavioural fact about Hi-Lo. It is explicable as an outcome of group identification by the players, because this is likely to produce a way of reasoning, team reasoning, that at once yields A. Team reasoning satisfies the conditions for the mode-P reasoning that we concluded in chapter 1 must be operative if people are ever to reason their way to A. It avoids magical thinking. It takes the profile-selection problem by the scruff of the neck. What explains its onset is an agency transformation in the mind of the player; this agency transformation leads naturally to profile-based reasoning and is a natural consequence of self-identification with the player group. (pg 142)
• Hi-Lo induces group identification. A bit more fully: the circumstances of Hi-Lo cause each player to tend to group-identify as a member of the group G whose membership is the player-set and whose goal is the shared payoff. (pg 142)
• If what induces A-choices is a piece of reasoning which is part of our mental constitution, we are likely to have the impression that choosing A is obviously right. Moreover, if the piece of reasoning does not involve a belief that the coplayer is bounded, we will feel that choosing A is obviously right against a player as intelligent as ourselves; that is, our intuitions will be an instance of the judgemental fact. I suspect, too, that if the reasoning schema we use is valid, rather than involving falacy, our intuitions of reality are likely to be more robust. Later I shall argue that team reasoning is indeed nonfallacious. (pg 143)
  • I think this is more than “as intelligent as ourselves”, I think this is a position/orientation/velocity case. I find it compelling that people with different POVs regard each other as ‘stupid’
  • When framing tendencies are culture-wide, people in whom a certain frame is operative are aware that it may be operative in others; and if its availability is high, those in it think that it is likely to be operative in others. Here the framing tendency is-so goes my claim-universal, and a fortiori it is culture-wide. (pg 144)
  • But for the theory of endogenous team reasoning there are two differences between the Hi-Lo case and these other cases of strong interdependence. First, outside Hi-Los there are counterpressures towards individual self-identification and so I-framing of the problem. In my model this comes out as a reduction in the salience of the strong interdependence, or an increase in that of other features. One would expect these pressures to be very strong in games like Prisoner’s Dilemma, and the fact that C rates are in the 40 per cent range rather than the 90 percent range, so far from surprising, is a prediction of the present theory (pg 144)
    • This is where MB starts to get to explore/exploit in populations. There are pressueres that drive groups together and apart. And as individuals, our thresholds for group identification varies
• Now it is the case, and increasingly widely recognized to be, that in games in general there’s no way players can rationally deliberate to a Nash equilibrium. Rather, classical canons of rationality do not in general support playing in Nash equilibria. So it looks as though shared intentions cannot, in the general run of games, by classical canons, be rationally formed! And that means in the general run of life as well. This is highly paradoxical if you think that rational people can have shared intentions. The paradox is not resolved by the thought that when they do, the context is not a game: any situation in which people have to make the sorts of decisions that issue in shared intentions must be a game, which is, after all, just a situation in which combinations of actions matter to the combining parties. (pg 139)
• Turn to the idea that a joint intention to do (x,y) is rationally produced in 1 and 2 by common knowledge of two conditional intentions: Pl has the intention expressed by ‘I’ll do x if and only if she does y’, and P2 the counterpart one. Clearly P1 doesn’t have the intention to do x if and. only if P2 in fact does y whether or not Pl believes P2 will do y; the right condition must be along the lines of:
  (C1) P1 intends to do x if and only if she believes P2 will do y. (pg 139)
  • So this is in belief space, and belief is based on awareness and trust
• There are two obstacles to showing this, one superable, the other not, I think. First, there are two Nash equilibria, and nothing in the setup to suggest that some standard refinement (strengthening) of the Nash equilibrium condition will eliminate one. However, I suspect that my description of the situation could be refined without ‘changing the subject’. Perhaps the conditional intention Cl should really be ‘I’ll do x if and only if she’ll do y, and that’s what I would like best’. For example, if x and y are the two obligations in a contract being discussed, it is natural to suppose that Pl thinks that both signing would be better than neither signing. If we accept this gloss then the payoff structure becomes a Stag Hunt – Hi-Lo if both are worse off out of equilibrium than in the poor equilibrium (x’ ,y’). To help the cause of rationally deriving the joint intention (x,y), assume the Hi-Lo case. What are the prospects now? As I have shown in chapter 1, there is no chance of deriving (x,y) by the classical canons, and the only (so far proposed) way of doing to is by team reasoning. (pg 140)
• The nature of team reasoning, and of the conditions under which it is likely to be primed in individual agents, has a consequence that gives further support to this claim. This is that joint intentions arrived at by the route of team reasoning involve, in the individual agents, a ‘sense of collectivity’. The nature of team reasoning has this effect, because the team reasoner asks herself not ‘What should I do?’ but ‘What should we do?’ So, to team-reason, you must already be in a frame in which first-person plural concepts are activated. The priming conditions for team reasoning have this effect because, as we shall see later in this chapter, team reasoning, for a shared objective, is likely to arise spontaneously in an individual who is in the psychological state of group-identifying with the set of interdependent actors; and to self-identify as a member of a group essentially involves a sense of collectivity. (pg 141)
• One of the things that MB seems to be saying here is that group identification has two parts. First is the self-identification with the group. Second is the mechanism that supports that framing. You can’t belong to a group you don’t see.
• To generalize the notions of team mechanism and team to unreliable contexts, we need the idea of the profile that gets enacted if all the agents function under a mechanism. Call this the protocol delivered by the mechanism. The protocol is , roughly, what everyone is supposed to do, what everyone does if the mechanism functions without any failure. But because there may well be failures, the protocol of a mechanism may not get enacted, some agents not playing their part but doing their default actions instead. For this reason the best protocol to have is not in general the first-best profile o*. In judging mechanisms we must take account of the states of the world in which there are failures, with their associated probabilities. How? Put it this way: if we are choosing a mechanism, we want one that delivers the protocol that maximizes the expected value of U. (pg 131)
• Group identification is a framing phenomenon. Among the many different dimensions of the frame of a decision-maker is the ‘unit of agency’ dimension: the framing agent may think of herself as an individual doer or as part of some collective doer. The first type of frame is operative in ordinary game-theoretic, individualistic reasoning, and the second in team reasoning. The concept-clusters of these two basic framings center round ‘I/ she/he’ concepts and ‘we’ concepts respectively. Players in the two types of frame begin their reasoning with the two basic conceptualizations of the situation, as a ‘What shall I do?’ problem, and a ‘What shall we do?’ problem, respectively. (pg 137)
• A mechanism is a general process. The idea (which I here leave only roughly stated) is of a causal process which determines (wholly or partly) what the agents do in any simple coordination context. It will be seen that all the examples I have mentioned are of this kind; contrast a mechanism that applies, say, only in two-person cases, or only to matching games, or only in business affairs. In particular, team reasoning is this kind of thing. It applies to any simple coordination context whatsoever. It is a mode of reasoning rather than an argument specific to a context. (pg 126)
• In particular, [if U is Paretian] the correct theory of Hi-Lo says that all play A. In short, an intuition in favour of C’ supports A-playing in Hi-Lo if we believe that all players are rational and there is one rationality. (pg 130)
  • Another form of dimension reduction – “We are all the same”

• There are many conceivable team mechanisms apart from simple direction and team reasoning; they differ in the way in which computation is distributed and the pattern of message sending. For example, one agent might compute o* and send instructions to the others. With the exception of team reasoning, these mechanisms involve the communication of information. If they do I shall call them modes of organization or protocols. (pg 125)
• A mechanism is a general process. The idea (which I here leave only roughly stated) is of a causal process which determines (wholly or partly) what the agents do in any simple coordination context. It will be seen that all the examples I have mentioned are of this kind; contrast a mechanism that applies, say, only in two-person cases, or only to matching games, or only in business affairs. In particular, team reasoning is this kind of thing. It applies to any simple coordination context whatsoever. It is a mode of reasoning rather than an argument specific to a context. (pg 126)
•  .
  •  (page 102)
  •  (pg 107)
  •  (pg 107)
• Evolutionary reasons for cooperation as group fitness, where group payoff is maximized. This makes the stag salient in stag hunt.
• Explaining the evolution of any human behavior trait (say, a tendency to play C in Prisoner’s Dilemmas) raises three questions. The first is the behavior selection question: why did this trait, rather than some other, get selected by natural selection? Answering this involves giving details of the selection process, and saying what made the disposition confer fitness in the ecology in which selection took place. But now note that ‘When a behavior evolves, a proximate mechanism also must evolve that allows the organism to produce the target behavior. Ivy plants grow toward the light. This is a behavior, broadly construed. For phototropism to evolve, there must be some mechanism inside of ivy plants that causes them to grow in one direction rather than in another’ (Sober and Wilson 1998, pp. 199-200). This raises the second question, the production question: how is the behavior produced within the individual-what is the ‘proximate mechanism’? In the human case, the interest is often in a psychological mechanism: we ask what perceptual, affective and cognitive processes issue in the behavior. Finally, note that these processes must also have evolved, so an answer to the second question brings a third: why did this proximate mechanism evolve rather than some other that could have produced the same behavior? This is the mechanism selection question. (pg 95)
  • These are good questions to answer, or at least address. Roughly, I thing my answers are
    • Selection Question: The three phases are a very efficient way to exploit an environment
    • Production Question: Neural coupling, as developed in physical swarms and moving on to cognitive clustering
    • Mechanism Question: Oscillator frequency locking provides a natural foundation for  collective behavior. Dimension reduction is how axis are selected for matching.
• “We need to know, in detail, what deliberations are like that people engage in when they group-identify”. Also, agency transformation. 
• Dimension reduction is a form of induced conceptual myopia (pg 89)? 
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