Notes: Chapter 18: Optionality
Chapter notes for “Chapter 18: Optionality”
Notes
1 Nassim Nicholas Taleb, Antifragile: Things That Gain from Disorder (2012). Taleb’s framework distinguishes systems that are harmed by volatility from those that benefit from it.
2 A.D. Wissner-Gross and C.E. Freer, “Causal Entropic Forces,” Physical Review Letters 110 (2013): 168702. This paper proposes that intelligent behavior can emerge from the maximization of future possibilities.
3 Indy Johar, “Civilizational Optioneering,” Long Now Foundation Seminar, January 27, 2026. https://longnow.org/talks/02026-johar/. Johar’s framework reframes environmental and systemic action as enlightened self-interest rather than moral obligation.
4 Samo Burja, “Intellectual Dark Matter,” Long Now Foundation Seminar (2019). Burja’s concept of scale-dependent knowledge describes capabilities that exist only because a global consumer market makes them viable. When the scale collapses, as with Roman luxury goods or medieval precision instruments, the knowledge evaporates within a generation.
5 Kevin Kelly, “The History and Future of Science,” Long Now Foundation lecture, 2006. Kelly argues that science generates possibilities rather than converging on truth: “Science is about expanding ignorance… the field of what you don’t know is expanding faster than what you’re learning.” See also What Technology Wants (Viking, 2010) and The Inevitable (Viking, 2016), especially on infinite games and the technium’s drive toward diversity.
6 Sam Vaknin, “Psychopaths: Dereistic Thinking and Enactivism” (2024), https://www.youtube.com/watch?v=i5xvCjZDsVU. Vaknin observes that healthy people experience reality’s infinitude as freedom—“so many possibilities and potentialities that one could never explore and discover”—while psychopaths perceive the identical reality as imprisonment. The concept of dereistic thinking originates with Eugen Bleuler (1919): fantasy-based cognition directed outward. The optionality blindness concept developed here is ours, extending Vaknin’s clinical observation into the optionality framework: the pathology lives in the agent’s capacity to perceive degrees of freedom within the environment, rather than in the environment itself.
7 Hofstadter, Douglas R., Gödel, Escher, Bach: An Eternal Golden Braid (1979). Basic Books. Hofstadter’s reframing of free will as a question about choice-making capacity rather than metaphysical libertarianism provides the conceptual foundation for grounding optionality ethics without solving the hard problem of free will.
7a Kolchinsky, A. and Wolpert, D.H., “Semantic information, autonomous agency and non-equilibrium statistical physics,” Interface Focus 8(6) (2018): 20180041.
8 Walker, Sara Imari, Life as No One Knows It: The Physics of Life’s Emergence (2024). Riverhead Books. Walker’s argument that the combinatorial space of possible configurations so vastly exceeds what present information could specify that the universe is “undeterministic”—genuinely open at the complex level — provides physical grounding for the claim that optionality is not merely a human preference but a feature of reality.
9 The Feynman-Kac formula connects the path integral formulation of quantum mechanics to the pricing of contingent claims in financial mathematics. Both compute expectation values by summing over all possible paths weighted by appropriate measures — phase factors in quantum mechanics, risk-neutral probabilities in finance. The structural identity is mathematical, not metaphorical. See Feynman, R.P., “Space-Time Approach to Non-Relativistic Quantum Mechanics,” Reviews of Modern Physics 20(2) (1948): 367–387, and Kac, M., “On Distributions of Certain Wiener Functionals,” Transactions of the American Mathematical Society 65(1) (1949): 1–13.
9b Steve Pressé, Kingshuk Ghosh, Julian Lee, and Ken A. Dill, “Principles of Maximum Entropy and Maximum Caliber in Statistical Physics,” Reviews of Modern Physics 85 (2013): 1115-1156. Maximum Caliber extends Jaynes’s Maximum Entropy to trajectory space: the least biased distribution over paths is the one that maximizes path entropy subject to constraints on time-averaged quantities. This single principle recovers Onsager’s reciprocal relations, the Green-Kubo transport coefficients, and Prigogine’s minimum entropy production theorem as special cases. Feynman-Kac is an instance. So is the causal entropy maximisation that Wissner-Gross described. The chain runs: optionality maximisation (this chapter) → path entropy maximisation (Maximum Caliber) → exponential thermodynamic weighting (Crooks). See the Online Annex, “The Path Integral Foundation,” for the full deductive chain from Onsager-Machlup through Crooks to the Trust Attractor.
9c Gavin E. Crooks, “Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences,” Physical Review E 60 (1999): 2721-2726. The ratio of the probability of a forward trajectory to the probability of its time-reverse is exp(ΔS), where ΔS is the entropy produced along the path. Applied to optionality: systems that preserve accessible futures (producing entropy) are exponentially more probable than those that foreclose them (consuming entropy). This makes the stability argument of Chapters 17-18 quantitative.
10a Cotler, Jordan, and Andrew Strominger, “The Universe as a Quantum Encoder,” arXiv:2201.11658 (2022). In an expanding universe, the Hilbert space of possibilities grows with the spatial volume, so quantum evolution cannot be unitary (which requires a fixed-size Hilbert space). The correct framework is isometry: a transformation that preserves inner products while mapping a smaller space into a larger one. Isometric evolution allows new quantum states to emerge (states with no valid pre-image in the past) while maintaining the mathematical consistency that originally motivated unitarity. The insight connects to Giddings’ “history matters” principle: not all formally possible configurations of an expanded Hilbert space are physically realisable; only those constructible from valid histories.
10b Robert M. Hazen, Michael L. Wong, et al., “On the roles of function and selection in evolving systems,” Proceedings of the National Academy of Sciences 120(43) (2023): e2310223120. The team proposes functional information as a unifying measure across minerals, stellar nucleosynthesis, and biology — arguing that selection for function drives complexity increases in all evolving systems, not merely biological ones. Wong frames the implication: “Information itself might be a vital parameter of the cosmos, similar to mass, charge and energy.” See also Philip Ball, “Why Everything in the Universe Turns More Complex,” Quanta Magazine (April 2, 2025), for an overview of the debate and its connections to assembly theory and Lee Cronin’s assembly index.
10c Paul Davies and colleagues have suggested that evolution in an expanding phase space may be formally equivalent to Gödel’s incompleteness theorems — the system is self-referential, generating possibilities that cannot be predicted from within the existing state. Kauffman’s “adjacent possible” (1996) prefigures this: each evolutionary step creates new adjacencies that did not exist before. The formal connection to incompleteness remains speculative but suggestive. See also Kauffman, Stuart A., “Answering Schrödinger’s ‘What is Life?’” Entropy 22(8) (2020): 815, on the unprestatable nature of biological adaptations.
10d Chaitin, Gregory, Proving Darwin: Making Biology Mathematical (2012). Vintage Books. For Zenil’s computational test of the algorithmic complexity framework: Zenil, H. et al., “An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems,” iScience 19 (2019): 1160-1172; and Zenil, H. et al., “Causal deconvolution by algorithmic generative models,” Nature Machine Intelligence 1 (2019): 58-66. The evolution experiment showing that complexity-biased mutations accelerate network evolution: Zenil, H., Kiani, N.A., and Tegnér, J., “Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations,” Royal Society Open Science 6 (2019): 181838. Albantakis’s observation on structured mutation search: quoted in Cepelewicz, J., “Mathematical Simplicity May Drive Evolution’s Speed,” Quanta Magazine (November 29, 2018). For a complementary finding that less than 5% of the human genome evolved by pure neutral drift — the remainder shaped by direct or linked selection: Pouyet, F. et al., “Background selection and biased gene conversion affect more than 95% of the human genome and bias demographic inferences,” eLife 7 (2018): e36317.
10e Craig R. White et al., “Metabolic scaling is the product of life-history optimization,” Science 377(6608) (2022): 834–839. White’s mathematical model shows that allometric scaling maximizes lifetime reproductive output without invoking geometric supply-network constraints. The connection to optionality: lifetime reproduction is the number of distinct future lineage configurations an organism’s genes can access. Maximizing descendants is maximizing optionality measured in genetic futures. The same optimization principle that the Trust Attractor identifies at the social scale (maximize systemic optionality) operates at the metabolic scale through natural selection.
10f White, C.R., Marshall, D.J., Alton, L.A., Arnold, P.A., Beaman, J.E., Bywater, C.L., Condon, C., Crispin, T.S., Janetzki, A., Pirber, E., Winwood-Smith, H.S., Angilletta, M.J., Chenoweth, S.F., Franklin, C.E., Halsey, L.G., Kearney, M.R., Kooijman, S.A.L.M., and Seebacher, F., “The role of metabolic rate in the evolution of life histories,” Biological Reviews 97(2) (2022): 768–785.
10 Smolin, Lee, “The dynamics of difference,” Foundations of Physics 48 (2018): 121–134; see also Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum (2019). Penguin Press. Smolin’s “causal theory of views” builds on Leibniz’s principle of the identity of indiscernibles: two events whose relational views are indistinguishable are, by definition, the same event. The principle of maximal variety, that nature acts to maximize the distinguishability of views, recovers quantum mechanics (the Schrödinger equation) from relational first principles, without background structure. The Leibniz quote is from The Monadology (1714), §57.
11 Still, S., D.A. Sivak, A.J. Bell, and G.E. Crooks, “Thermodynamics of prediction,” Physical Review Letters 109 (2012): 120604. The authors prove that any system driven by a fluctuating environment incurs a thermodynamic cost proportional to the mutual information between its state and past environmental states that are not predictive of the future. Wolpert’s estimate of cellular computational efficiency: Wolpert, D.H., “The stochastic thermodynamics of computation,” Journal of Physics A 52 (2019): 193001.
11a Fields, C. and Levin, M., “Metabolic limits on classical information processing by biological cells,” Biosystems 209: 104513 (2021).
12 Damasceno, A.P., M. Engel, and S.C. Glotzer, “Predictive Self-Assembly of Polyhedra into Complex Structures,” Science 337 (2012): 453–457. Glotzer’s group has since studied over 50,000 particle shapes, finding entropy-driven self-assembly into more than 50 known crystal space groups — without any attractive interactions. The quasicrystal formed by tetrahedra, first reported in Haji-Akbari, A., et al., “Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra,” Nature 462 (2009): 773–777, remains the most complex entropically stabilized structure observed.
12b Aditya Barve and Andreas Wagner, “A latent capacity for evolutionary innovation through exaptation in metabolic systems,” Nature 500 (2013): 203–206. The study modeled metabolic networks using the known 1,397-reaction E. coli network as a starting template, performing 5,000 random reaction swaps per network while maintaining viability on glucose. The result, that complexity inherently generates unused capabilities, provides quantitative grounding for Gould and Vrba’s concept of exaptation (see Chapter 7, note 9). The finding complements the Glotzer experiments on entropy-driven self-assembly: both demonstrate that structural richness generates functional possibility as an intrinsic property, not a selected outcome.
12a Chastain, Erick, Adi Livnat, Christos Papadimitriou, and Umesh Vazirani, “Algorithms, games, and evolution,” Proceedings of the National Academy of Sciences 111(29) (2014): 10620–10623. The authors show that the equations describing allele frequency changes in a sexually reproducing population under weak selection are mathematically identical to the multiplicative weights update algorithm — a method independently derived in computer science for online learning and game-theoretic optimization. The algorithm’s objective function maximizes a combination of mean fitness and Shannon entropy (genetic diversity), providing a formal basis for the claim that evolution values diversity intrinsically, not merely as a byproduct.
9d Amari, S., Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics 28 (Berlin: Springer, 1985); Ay, N., Jost, J., Lê, H.V. & Schwachhöfer, L., Information Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete 64 (Cham: Springer, 2017). The Fisher information metric endows the space of probability distributions with Riemannian (curved) geometry: each coordination strategy corresponds to a point on this manifold, and the Kullback-Leibler divergence (a measure of how much one probability distribution differs from another), which serves as the control cost in Kappen’s path-integral formulation of stochastic optimal control, measures geodesic distance between strategies. Amari (1985) established the differential-geometric foundations; Ay et al. (2017) provide the modern comprehensive treatment. In the chapter’s argument, this geometric structure gives “fragility of coordination” a precise meaning: the curvature of the information-geometric manifold at an equilibrium measures how much small perturbations amplify. High positive curvature means brittle, coercion-dependent coordination (small shocks produce large deviations); low or zero curvature means robust, invitation-based coordination (perturbations are absorbed). The Trust Attractor occupies the region of lowest curvature (the flattest part of the landscape), which is why it absorbs perturbation rather than amplifying it. This connects the optionality framework to information geometry: maximizing optionality is equivalent to finding trajectories that remain maximally distant from constraint boundaries in this curved space.
13a Bingham, E. and Ratcliff, W.C., “Prokaryotic genome streamlining as a barrier to complex multicellularity,” Proceedings of the National Academy of Sciences (2024). The computational model shows that organisms programmed to shrink genomes under drift cannot sustain the toolkit accumulation required for complex multicellularity, regardless of the fitness reward.
13b Lynch, M., “The origins of eukaryotic gene structure,” Molecular Biology and Evolution 23(2) (2006): 450–468. Lynch’s nonadaptive theory of genome evolution demonstrates that many features of eukaryotic genomes (introns, gene duplications, mobile elements) are consequences of reduced population size and weakened selection, not adaptations per se. See also Lynch, M., The Origins of Genome Architecture (Sinauer, 2007).
13c Lane, N. and Martin, W., “The energetics of genome complexity,” Nature 467 (2010): 929–934.
13 Xue, C. and Goldenfeld, N., “Coevolution Maintains Diversity in the Stochastic ‘Kill the Winner’ Model,” Physical Review Letters 119 (2017): 268101. Goldenfeld and Xue showed that the standard kill-the-winner model, when corrected for stochastic noise (the discreteness of individuals), collapses to total extinction. Adding coevolution (prey evolving resistance, predators evolving new attacks) rescues biodiversity through ongoing species generation. The implication: wherever predator-prey dynamics and evolution co-occur, diversity is the thermodynamic norm. See also their discussion of universality in Goldenfeld, N. and Woese, C., “Life is physics: evolution as a collective phenomenon far from equilibrium,” Annual Review of Condensed Matter Physics 2 (2011): 375–399.
14 Rossine, F.W., Martinez-Garcia, R., Sgro, A.E., Gregor, T., and Tarnita, C.E., “Eco-evolutionary significance of ‘loners,’” PLOS Biology 18(3) (2020): e3000642. The study found that the number of non-aggregating cells is maintained at a heritable set point (not a constant fraction), varies between strains, and is influenced by environmental factors affecting chemical signal diffusion. Earlier characterization: Tarnita, C.E. et al., “Fitness tradeoffs between spores and nonaggregating cells can explain the coexistence of diverse genotypes in cellular slime molds,” PNAS 112(9) (2015): 2776–2781.
14a Vakirlis, N., Acar, O., Hsu, B., Castilho Coelho, N., Van Oss, S.B., Wacholder, A., Meber, K., Ruber, C., Kirchner, A., Yoon, E., McLysaght, A., and Carvunis, A.-R., “De novo emergence of adaptive membrane proteins from thymine-rich genomic sequences,” Nature Communications 11 (2020): 781. Roughly 10% of overexpressed proto-gene sequences enhanced yeast colony growth — a higher rate of fitness benefit than overexpressing established genes. Beneficial proto-genes were enriched for predicted transmembrane domains. See also Vakirlis, N., Carvunis, A.-R., and McLysaght, A., “Synteny-based analyzes indicate that sequence divergence is not the main source of orphan genes,” eLife 9 (2020): e53500, which estimates that at most one-third of orphan genes can be explained by divergence beyond recognition; the remainder are candidates for de novo origin.