Determined, page 47
BACK TO NOTE REFERENCE 2
P. Anderson, “More Is Different,” Science 177 (1972): 393. Back to the fact that a single molecule of water cannot possess the property of “wetness”— it also cannot possess the property of surface tension (the emergent feature of water that allows basilisk Jesus lizards to run across the surface of a pond).
BACK TO NOTE REFERENCE 3
For an analysis of how people move in crowds in ways that resemble the fluid dynamics of waterfalls, see N. Bain and D. Bartolo, “Dynamic Response and Hydrodynamics of Polarized Crowds,” Science 363 (2019): 46. For something similar in ants, see A. Dussutour et al., “Optimal Travel Organization in Ants under Crowded Conditions,” Nature 428 (2003): 70.
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Footnote: Discussed at length in P. Hiesenger, The Self-Assembling Brain: How Neural Networks Grow Smarter (Princeton University Press, 2021).
BACK TO NOTE REFERENCE 5
M. Bedau, “Is Weak Emergence Just in the Mind?,” Minds and Machines 18 (2008): 443; J. Kim, “Making Sense of Emergence,” Philosophical Studies 95 (1999): 3; O. Sartenaer, “Sixteen Years Later: Making Sense of Emergence (Again),” Journal of General Philosophical Sciences 47 (2016): 79.
BACK TO NOTE REFERENCE 6
E. Bonabeau and G. Theraulaz, “Swarm Smarts,” Scientific American 282, no. 3 (2000): 72; M. Dorigo and T. Stutzle, Ant Colony Optimization (MIT Press, 2004); S. Garnier, J. Gautrais, and G. Theraulaz, “The Biological Principles of Swarm Intelligence,” Swarm Intelligence 1 (2007): 3 (note that this topic was the first paper published in the history of this journal, which kind of makes sense, given its title).
BACK TO NOTE REFERENCE 7
L. Chen, D. Hall, and D. Chklovskii, “Wiring Optimization Can Relate Neuronal Structure and Function,” Proceedings of the National Academy of Sciences of the United States of America 103 (2006): 4723; M. Rivera-Alba et al., “Wiring Economy and Volume Exclusion Determine Neuronal Placement in the Drosophila Brain,” Current Biology 21 (2011): 2000; J. White et al., “The Structure of the Nervous System of the Nematode Caenorhabditis elegans,” Philosophical Transactions of the Royal Society B, Biological Sciences 314 (1986): 1; V. Klyachko and C. Stevens, “Connectivity Optimization and the Positioning of Cortical Areas,” Proceedings of the National Academy of Sciences of the United States of America 100 (2003): 7937; G. Mitchison, “Neuronal Branching Patterns and the Economy of Cortical Wiring,” Proceedings of the Royal Society B: Biological Sciences 245 (1991): 151.
BACK TO NOTE REFERENCE 8
Y. Takeo et al., “GluD2- and Cbln1-Mediated Competitive Interactions Shape the Dendritic Arbor of Cerebellar Purkinje Cells,” Neuron 109 (2020): 629.
BACK TO NOTE REFERENCE 9
S. Camazine and J. Sneyud, “A Model of Collective Nectar Source Selection by Honey Bees: Self-Organization through Simple Rules,” Journal of Theoretical Biology 149 (1991): 547.
Footnote (p. 160): K. von Frisch, The Dancing Bees: An Account of the Life and Senses of the Honey Bee (Harvest Books, 1953).
BACK TO NOTE REFERENCE 10
P. Visscher, “How Self-Organization Evolves,” Nature 421 (2003): 799; M. Myerscough, “Dancing for a Decision: A Matrix Model for Net-Site Choice by Honey Bees,” Proceedings of the Royal Society of London B 270 (2003): 577; D. Gordon, “The Rewards of Restraint in the Collective Regulation of Foraging by Harvester Ant Colonies,” Nature 498 (2013): 91; D. Gordon, “The Ecology of Collective Behavior,” PLOS Biology 12, no. 3 (2014): e1001805. For additional studies in this area see: J. Deneubourg and S. Goss, “Collective Patterns and Decision Making,” Ethology Ecology and Evolution 1 (1989): 295; S. Edwards and S. Pratt, “Rationality in Collective Decision-Making by Ant Colonies,” Proceedings of the Royal Society B 276 (2009): 3655; E. Bonabeau et al., “Self-Organization in Social Insects,” Trends in Ecology and Evolution 12 (1997): 188.
Footnote: G. Sherman and P. Visscher, “Honeybee Colonies Achieve Fitness through Dancing,” Nature 419 (2002): 920.
Second footnote: R. Goldstone, M. Roberts, and T. Gureckis, “Emergent Processes in Group Behavior,” Current Directions in the Psychological Sciences 17 (2008): 10; C. Doctorow, “A Catalog of Ingenious Cheats Developed by Machine-Learning Systems,” BoingBoing, November 12, 2018, boingboing.net/2018/11/12/local-optima-r-us.html.
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C. Reid and M. Beekman, “Solving the Towers of Hanoi—How an Amoeboid Organism Efficiently Constructs Transport Networks,” Journal of Experimental Biology 216 (2013): 1546; C. Reid and T. Latty, “Collective Behaviour and Swarm Intelligence in Slime Moulds,” FEMS Microbiology Reviews 40 (2016): 798.
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S. Tero et al., “Rules for Biologically Inspired Adaptive Network Design,” Science 327 (2010): 439.
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For another example of slime molds, see L. Tweedy et al., “Seeing around Corners: Cells Solve Mazes and Respond at a Distance Using Attractant Breakdown,” Science 369 (2020): 1075.
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Footnote: Hiesenger, Self-Assembling Brain. For an example of repulsion, see D. Pederick et al., “Reciprocal Repulsions Instruct the Precise Assembly of Parallel Hippocampal Networks,” Science 372 (2021): 1058. See also: L. Luo, “Actin Cytoskeleton Regulation in Neuronal Morphogenesis and Structural Plasticity,” Annual Review of Cellular Developmental Biology 18 (2002): 601; J. Raper and C. Mason, “Cellular Strategies of Axonal Pathfinding,” Cold Spring Harbor Perspectives in Biology 2 (2010): a001933.
How do neurons, when connecting up, also figure out which part of a target neuron to connect to (proximal or distal spines, cell body, axon in case of some neurotransmitters)? Neurons have the ability to control which branches of their axonal processes receive proteins needed for synapse construction: S. Falkner and P. Scheiffele, “Architects of Neuronal Wiring,” Science 364 (2019): 437; O. Urwyler et al., “Branch-Restricted Localization of Phosphatase Prl-1 Specifies Axonal Synaptogenesis Domains,” Science 364 (2019): 454; E. Favuzzi et al., “Distinct Molecular Programs Regulate Synapse Specificity in Cortical Inhibitory Circuits,” Science 363 (2019): 413.
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T. More, A. Buffo, and M. Gotz, “The Novel Roles of Glial Cells Revisited: The Contribution of Radial Glia and Astrocytes to Neurogenesis,” Current Topics in Developmental Biology 69 (2005): 67; P. Malatesta, I. Appolloni, and F. Calzolari, “Radial Glia and Neural Stem Cells,” Cell and Tissue Research 331 (2008): 165; P. Oberst et al., “Temporal Plasticity of Apical Progenitors in the Developing Mouse Neocortex,” Nature 573 (2019): 370.
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For an example of the molecular biology of the exquisite timing that goes into neuron interactions with radial glia, see K. Yoon et al., “Temporal Control of Mammalian Cortical Neurogenesis by m6A Methylation,” Cell 171 (2017): 877.
Footnote: N. Ozel et al., “Serial Synapse Formation through Filopodial Competition for Synaptic Seeding Factors,” Developmental Cell 50 (2019): 447; M. Courgeon and C. Desplan, “Coordination between Stochastic and Deterministic Specification in the Drosophila Visual System,” Science 366 (2019): 325.
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T. Huxley, “On the Hypothesis That Animals Are Automata, and Its History,” Nature 10 (1874): 362. Amid all these references to recent, cutting-edge science, it’s kind of charming to reference a nineteenth-century scientific publication.
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For more on this general topic, see the fantastic J. Gleick, Chaos: Making a New Science (Viking, 1987).
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Forty-eight thousand miles: J. Castro, “11 Surprising Facts about the Circulatory System,” LiveScience, August 8, 2022, livescience.com/39925-circulatory-system-facts-surprising.html.
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The basis of this model: D. Iber and D. Menshykau, “The Control of Branching Morphogenesis,” Open Biology 3 (2013): 130088130088; D. Menshykau, C. Kraemer, and D. Iber, “Branch Mode Selection during Early Lung Development,” PLOS Computational Biology 8 (2012): e1002377. For an exploration of these issues at the laboratory bench, see R. Metzger et al., “The Branching Programme of Mouse Lung Development,” Nature 453 (2008): 745.
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A. Lindenmayer, “Developmental Algorithms for Multicellular Organisms: A Survey of L-Systems,” Journal of Theoretical Biology 54 (1975): 3.
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A. Ochoa-Espinosa and M. Affolter, “Branching Morphogenesis: From Cells to Organs and Back,” Cold Spring Harbor Perspectives in Biology 4 (2004): a008243; P. Lu and Z. Werb, “Patterning Mechanisms of Branched Organs,” Science 322 (2008): 1506–9.
Footnote: A. Turing, “The Chemical Basis of Morphogenesis,” Philosophical Transactions of the Royal Society of London B 237 (1952): 37.
Second footnote: E. Azpeitia et al., “Cauliflower Fractal Forms Arise from Perturbations of Floral Gene Networks,” Science 373 (2021): 192.
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G. Vogel, “The Unexpected Brains behind Blood Vessel Growth,” Science 307 (2005): 665; Metzger et al., “Branching Programme of Mouse Lung Development”; P. Carmeliet and M. Tessier-Lavigne, “Common Mechanisms of Nerve and Blood Vessel Wiring,” Nature 436 (2005): 193. The second author, the superb neurobiologist and my departmental colleague Marc Tessier-Lavigne, expanded his portfolio a few years back and became president of Stanford University.
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J. Bassingthwaighte, L. Liebovitch, and B. West, Fractal Physiology, Methods in Physiology (American Physiological Society, 1994).
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“The World Religions Tree,” 000024.org/religions_tree/religions_tree_8.html [inactive].
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E. Favuzi et al., “Distinct Molecular Programs Regulate Synapse Specificity in Cortical Inhibitory Circuits,” Science 363 (2019): 413; V. Hopker et al., “Growth-Cone Attraction to Netrin-1 Is Converted to Repulsion by Laminin-1,” Nature 401 (1999): 69; J. Dorskind and A. Kolodkin, “Revisiting and Refining Roles of Neural Guidance Cues in Circuit Assembly,” Current Opinion in Neurobiology 66 (2020): 10; S. McFarlane, “Attraction vs. Repulsion: The Growth Cones Decides,” Biochemistry and Cell Biology 78 (2000): 563.
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A. Bassem, A. Hassan, and P. R. Hiesinger, “Beyond Molecular Codes: Simple Rules to Wire Complex Brains,” Cell 163 (2015): 285. For a two-rule system built around mechanical constraints explaining one aspect of human brain development, see E. Karzbrun et al., “Human Neural Tube Morphogenesis in Vitro by Geometric Constraints,” Nature 599 (2021): 268.
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D. Miller et al., “Full Genome Viral Sequences Inform Patterns of SARS-CoV-2 Spread into and within Israel,” Nature Communications 11 (2020): 5518; D. Adam et al., “Clustering and Superspreading Potential of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Infections in Hong Kong,” Nature Medicine 26 (2020): 1714.
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General reviews: A. Barabasi, “Scale-Free Networks: A Decade and Beyond,” Science 325 (2009): 412; A. Barabasi and R. Albert, “Emergence of Scaling in Random Networks,” Science 286 (1999): 509; C. Song, S. Havlin, and H. Makse, “Self-Similarity of Complex Networks,” Nature 433 (2005): 392; P. Drew and L. Abbott, “Models and Properties of Power-Law Adaptation in Neural Systems,” Journal of Neurophysiology 96 (2006): 826.
Power law and related distributions in the brain: G. Buzsaki and A. Draguhn, “Neuronal Oscillations in Cortical Networks,” Science 304 (2004): 1926; Power laws and the number of neurotransmitter vesicles released in response to an action potential: J. Lamanna et al., “A Pre-docking Source for the Power-Law Behavior of Spontaneous Quantal Release: Application to the Analysis of LTP,” Frontiers of Cellular Neuroscience 9 (2015): 44.
Power law distributions and:
Spread of Covid: D. Miller et al., “Full Genome Viral Sequences Inform Patterns of SARS-CoV-2 Spread into and within Israel,” Nature Communications 11 (2020): 5518; D. Adam et al., “Clustering and Superspreading Potential of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Infections in Hong Kong,” Nature Medicine 26 (2020): 1714.
Earthquakes: F. Meng, L. Wong, and H. Zhou, “Power Law Relations in Earthquakes from Microscopic to Macroscopic Scales,” Scientific Reports 9 (2019): 10705.
Warfare and hate groups: N. Gilbert, “Modelers Claim Wars Are Predictable,” Nature 462 (2009): 836; N. Johnson et al., “Hidden Resilience and Adaptive Dynamics of the Global Online Hate Ecology,” Nature 573 (2019): 261; M. Schich et al., “Quantitative Social Science: A Network Framework of Cultural History,” Science 345 (2014): 558.
Here’s a topic that I barely understand, but I want to show off that I was able to force myself through a number of papers on the subject. A pattern can be highly structured, with repeating building blocks; its signal in a frequency spectrum is termed “white noise.” This is akin to tight, uniform little interconnected clusters of neurons, isolated from each other. At the other extreme, a pattern that is random produces “brown noise” (named for Brownian motion, explained in chapter 9); these are connections between neurons of random distances, directions, and strengths. And as with porridge that is neither too hot nor too cold, there are patterns poised between the two extremes, termed “pink noise” (or 1/f noise). These are the networks of the brain balanced in scale-free ways between the robustness and efficiency of small, structured local networks and the creativity and evolvability of long-distance ones. The “critical brain” hypothesis posits that brains have evolved to be at this ideal spot and that this “criticality” optimizes all sorts of features of brain function. Moreover, in this model, the brain is able to correct itself as that perfect balancing point shifts with circumstances; this would be an example of the very trendy “self-organized criticality.” This can be shown with some mathematically bruising analytical techniques, and a small subfield has grown examining brain criticality in normal and diseased circumstances. For example, there is a tilt toward white noise in epilepsy, reflecting the overly synchronized firing of clusters of epileptiform neurons (and, in fact, there is a remarkable similarity between the distribution of frequency and severity of seizures, and that of earthquakes). Similarly, autism spectrum disorder appears to have a different type of tilt toward white noise, reflecting the relatively isolated peninsulas of function in the cortex. And at the other end, Alzheimer’s disease involves a tilt toward brown noise, as the death of neurons here and there begins to break down the patterning (and efficacy) of networks. See: J. Beggs and D. Plenz, “Neuronal Avalanches in Neocortical Circuits,” Journal of Neuroscience 23 (2003): 11167; P. Bak, C. Tang, and K. Wiesenfeld, “Self-Organized Criticality: An Explanation of the 1/f Noise,” Physics Review Letters 59 (1987): 381; L. Cocchi et al., “Criticality in the Brain: A Synthesis of Neurobiology, Models and Cognition,” Progress in Neurobiology 158 (2017): 132; M. Gardner, “White and Brown Music, Fractal Curves and One-Over-f Fluctuation,” Scientific American, April 1978; M. Belmonte et al., “Autism and Abnormal Development of Brain Connectivity,” Journal of Neuroscience 24 (2004): 9228.
Footnote: A website celebrating the mathematics of Bacon numbers: coursehero.com/file/p12lp1kl/chosen-actors-can-be-linked-by-a-path-through-Kevin-Bacon-in-an-average-of-6/. For an excellent, accessible biography of Paul Erdös, see P. Hoffman, The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth (Hyperion, 1998).
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For an example, see J. Couzin et al., “Effective Leadership and Decision-Making in Animal Groups on the Move,” Nature 433 (2005): 7025.
Footnote: For example, see C. Candia et al., “The Universal Decay of Collective Memory and Attention,” Nature Human Behaviour 3 (2018): 82. Also see V. Verbavatz and M. Barthelemy, “The Growth Equation of Cities,” Nature 587 (2020): 397.
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C. Song, S. Havlin, and H. Makse, “Self-Similarity of Complex Networks,” Nature 433 (2005): 392.
Emergence in ecological contexts: M. Buchanan, “Ecological Modeling: The Mathematical Mirror to Animal Nature,” Nature 453 (2008): 714; N. Humphries et al., “Environmental Context Explains Levy and Brownian Movement Patterns of Marine Predators,” Nature 465 (2010): 1066; J. Banavar et al., “Scaling in Ecosystems and the Linkage of Macroecological Laws,” Physical Review Letters 98 (2007): 068104; B. Houchmandzadeh and M. Vallade, “Clustering in Neutral Ecology,” Physical Reviews E 68 (2003): 061912.
