The Entropic Brain

1. 1

   Note 1. Karl Friston, “The free-energy principle: a unified brain theory?” Nature Reviews Neuroscience 11 (2010): 127-138. The Free Energy Principle reframes cognition as prediction-error minimization.

2. 1b

   Note 1b. Karl Friston, Lancelot Da Costa, Dalton A.R. Sakthivadivel, Conor Heins, Grigorios A. Pavliotis, Maxwell Ramstead, and Thomas Parr, “Path Integrals, Particular Kinds, and Strange Things,” Physics of Life Reviews 47 (2023): 35-62. Explicit path integral formulation of the Free Energy Principle. The brain minimizes a path integral of free energy over sensorimotor histories — an instance of Maximum Caliber (Pressé et al. 2013): maximizing the entropy of accessible trajectories subject to constraints. Kappen (2005) showed independently that optimal stochastic control reduces to path integral inference, with control cost measured as the KL divergence from passive dynamics (how far the controlled distribution of paths departs from the uncontrolled one). That result lets this book connect the brain’s prediction machinery to the coordination dynamics of Chapter 17. See 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): 1115-1141; and Hilbert J. Kappen, “Path Integrals and Symmetry Breaking for Optimal Control Theory,” Journal of Statistical Mechanics (2005): P11011.

3. 2

   Note 2. Robin L. Carhart-Harris et al., “The entropic brain: a theory of conscious states informed by neuroimaging research with psychedelic drugs,” Frontiers in Human Neuroscience 8 (2014): 20.

4. 3

   Note 3. For empirical support, see Carhart-Harris et al., “Neural correlates of the LSD experience revealed by multimodal neuroimaging,” PNAS 113 (2016): 4853-4858.

5. 4

   Note 4. Calvin Ly et al., “Psychedelics Promote Structural and Functional Neural Plasticity,” Cell Reports 23 (2018): 3170-3182. This study demonstrated that psychedelics stimulate neuritogenesis and spinogenesis through TrkB and mTOR signaling pathways in cultured neurons and animal models, a candidate mechanism for their therapeutic effects.

6. 5

   Note 5. Link Swanson, “Unifying Theories of Psychedelic Drug Effects,” Frontiers in Pharmacology 9 (2018): 172. Swanson’s meta-review shows how the entropic brain hypothesis, Integrated Information Theory, and predictive processing frameworks converge on the same core principle.

7. 6

   Note 6. Tim Urban, “Neuralink and the Brain’s Magical Future,” Wait But Why (2017). The essay pictures humanity as a single collective organism, the “Human Colossus,” whose thinking runs through the networked brains of its members.

8. 7

   Note 7. Selen Atasoy et al., “Connectome-harmonic decomposition of human brain activity reveals dynamical repertoire re-organization under LSD,” Scientific Reports 7 (2017): 17661. The connectome harmonics framework decomposes brain activity into spatial patterns (analogous to musical overtones) defined by the brain’s structural wiring, providing a geometric approach to understanding brain dynamics.

9. 8

   Note 8. Jeremy England, “Dissipative adaptation in driven self-assembly,” Nature Nanotechnology 10 (2015): 919-923. England’s work proposes that driven systems spontaneously organize to resonate with external energy sources.

10. 9

    Note 9. The “neuronal entropy maximization” hypothesis proposes that neurons are best understood as agents maximizing their influence on the network rather than as information processors. It was set out in an unpublished working paper by Roshawn Terrell and the author: Terrell, R. and Watson, N., “Neuronal Entropy Maximization: A Proposed New Model for Neural Networks” (2016), and is offered as a hypothesis rather than an established result. “The Entropic Neuron” develops it further. Friston’s Free Energy Principle (note 1) is a related account but not the same one: it has the brain minimize free energy rather than maximize entropy.

11. 11

    Note 11. James P. Crutchfield, “Space-Time Dynamics in Video Feedback,” Physica D 10 (1984): 229-245. Crutchfield showed that video feedback dynamics closely resemble reaction-diffusion systems and biological morphogenesis. See also James D. Murray, Mathematical Biology (Springer, 1993) for the foundational treatment of morphogenetic pattern formation.

12. 12

    Note 12. Andy Clark and David J. Chalmers, “The Extended Mind,” Analysis 58:1 (1998): 7-19. This influential paper argued that cognitive processes can extend beyond the brain into the environment, incorporating external tools and artifacts as literal parts of cognitive systems.

13. 13

    Note 13. Andrey Kolmogorov, “On Tables of Random Numbers,” Sankhyā: The Indian Journal of Statistics Series A 25:4 (1963): 369-376. Kolmogorov complexity (the length of the shortest program producing a string) makes pattern and randomness precise: a patterned string compresses into a short program, and a random one does not. See also Gregory Chaitin’s work on algorithmic information theory.

14. 15

    Note 15. Daniel Kahneman, Thinking, Fast and Slow (2011). Kahneman’s synthesis of decades of work with Amos Tversky popularized the distinction between System 1 (fast, intuitive) and System 2 (slow, deliberative) thinking. See also Keith Stanovich and Richard West, “Individual differences in reasoning: Implications for the rationality debate?” Behavioral and Brain Sciences 23 (2000): 645-665 for the theoretical foundations.

15. 16

    Note 16. George Lakoff and Mark Johnson, Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought (1999). This work argues that abstract concepts are grounded in bodily metaphors. See also Andy Clark, Being There: Putting Brain, Body, and World Together Again (1997) for the situated cognition perspective, and Lawrence Shapiro, Embodied Cognition (2010) for a philosophical overview of the field.

16. 17

    Note 17. R. Guevara Erra, D. M. Mateos, R. Wennberg, and J. L. Perez Velazquez, “Statistical mechanics of consciousness: Maximization of information content of network is associated with conscious awareness,” Physical Review E 94 (2016): 052402. This study analyzed neurophysiological recordings across conscious and unconscious states, finding that wakeful awareness corresponds to maximum entropy in brain network configurations.

17. 17a

    Note 17a. Michael M. Schartner et al., “Increased spontaneous MEG signal diversity for psychoactive doses of ketamine, LSD and psilocybin,” Scientific Reports 7 (2017): 46421.

18. 18

    Note 18. D. Chang, D. Song, J. Zhang, Y. Shang, Q. Ge, and Z. Wang, “Caffeine caused a widespread increase of resting brain entropy,” Scientific Reports 8 (2018): 2700. This study demonstrated that caffeine increases brain entropy despite reducing cerebral blood flow, suggesting the entropy effect is neuronal rather than vascular.

19. 18a

    Note 18a. Thomas Donoghue, Matar Haller, Erik J. Peterson, Paroma Varma, Priyadarshini Sebastian, Richard Gao, Torben Noto, Antonio H. Lara, Joni D. Wallis, Robert T. Knight, Avgusta Shestyuk, and Bradley Voytek, “Parameterizing neural power spectra into periodic and aperiodic components,” Nature Neuroscience 23:12 (2020): 1655–1665.

20. 18b

    Note 18b. Janna D. Lendner, Randolph F. Helfrich, Bryce A. Mander, Luis Romundstad, Jack J. Lin, Matthew P. Walker, Pal G. Larsson, and Robert T. Knight, “An electrophysiological marker of arousal level in humans,” eLife 9 (2020): e55092. The slope of the aperiodic (1/f) EEG signal distinguishes wakefulness from sleep, including REM sleep, which traditional oscillatory measures cannot separate from wakefulness. The authors propose the aperiodic slope as an objective marker of arousal level.

21. 18c

    Note 18c. Bradley Voytek, Mark A. Kramer, John Case, Kyle Q. Lepage, Zechari R. Tempesta, Robert T. Knight, and Adam Gazzaley, “Age-Related Changes in 1/f Neural Electrophysiological Noise,” Journal of Neuroscience 35:38 (2015): 13257–13265. With age, the aperiodic (1/f) component of neural activity flattens toward white noise, and the degree of flattening correlates with working-memory decline.

22. 20

    Note 20. Harry Law, “Faster Horses,” Cosmos Institute blog, January 2, 2026, https://blog.cosmos-institute.org/p/faster-horses. The wording is Law’s own, summarizing Marvin Minsky’s society of mind: “For Minsky, intelligence emerges from many mindless ‘agents’ coordinated in special ways, with the mind employing something like a computational and explanatory strategy whose power is a product of messiness, cross-connection, coordination, and resolution.” For Minsky’s original statement of the idea, see Marvin Minsky, The Society of Mind (Simon and Schuster, 1986). The picture echoes the entropic brain hypothesis at a different scale: minds require neither pure order nor pure chaos, only the critical edge where coordination produces emergent capability.

23. 21

    Note 21. Max S. Bennett, “Five Breakthroughs: A First Approximation of Brain Evolution From Early Bilaterians to Humans,” Frontiers in Neuroanatomy 15 (2021): 693346, https://doi.org/10.3389/fnana.2021.693346. Bennett synthesizes comparative psychology, evolutionary neuroscience, and AI research to trace the “five breakthroughs” that produced human cognition. See also Bennett, “What Behavioral Abilities Emerged at Key Milestones in Human Brain Evolution? 13 Hypotheses on the 600-Million-Year Phylogenetic History of Human Intelligence,” Frontiers in Psychology 12 (2021): 685853, https://doi.org/10.3389/fpsyg.2021.685853. These papers form the foundation for his book A Brief History of Intelligence (HarperCollins, 2023).

24. 22

    Note 22. The regret result is Steiner, A.P. and Redish, A.D., “Behavioral and neurophysiological correlates of regret in rat decision-making on a neuroeconomic task,” Nature Neuroscience 17(7) (2014): 995–1002. DOI: 10.1038/nn.3740. On the “Restaurant Row” task, when a rat skipped a good offer and then met a worse one, neurons in orbitofrontal cortex and ventral striatum transiently represented the foregone option, and the rat changed its later choices accordingly. The hippocampal contribution is a separate phenomenon: at a choice point, place-cell ensembles sweep forward along the routes under consideration before the animal commits (Johnson, A. and Redish, A.D., “Neural ensembles in CA3 transiently encode paths forward of the animal at a decision point,” Journal of Neuroscience 27(45) (2007): 12176–12189. DOI: 10.1523/JNEUROSCI.3761-07.2007). Whether this counterfactual machinery serves forward planning is contested: hippocampal replay content tracks specific past experiences and can run counter to the animal’s next choice (Gillespie, A.K. et al., “Hippocampal replay reflects specific past experiences rather than a plan for subsequent choice,” Neuron 109(19) (2021): 3149–3163. DOI: 10.1016/j.neuron.2021.07.029). A. David Redish, The Mind within the Brain: How We Make Decisions and How Those Decisions Go Wrong (Oxford University Press, 2013), gives the accessible synthesis.

25. 23

    Note 23. Amato, K.R., DeCasien, A.R., Aronoff, J.E., et al., “Primate gut microbiota induce evolutionarily salient changes in mouse neurodevelopment,” PNAS (2026). Mice colonized with microbiomes from large-brained primates (humans, squirrel monkeys) showed upregulation of oxidative phosphorylation genes in frontal cortex — the metabolic infrastructure for high-demand neural computation. The study suggests that gut microbes can shift the brain’s metabolic gene expression, one possible route by which microbial partners contribute to neural capacity.

26. 24

    Note 24. Xiangyi Meng, Albert-László Barabási, et al., “Surface optimization governs the local design of physical networks,” Nature 649(8096) (2026). Using mathematical tools from string theory (high-dimensional Feynman diagrams), the researchers showed that biological networks optimize surface area in three dimensions, not just path length. The prediction of trifurcations and stable orthogonal branches matches observed neural architecture — 98% of right-angle sprouts in human brain data end in synapses.

27. 25

    Note 25. Rodrick Wallace, “Fog, Friction, Delay and the Failure of Bounded Rationality Embodied Cognition: A formal study of generalized psychopathology,” preprint submitted to Elsevier (January 2026). Wallace’s mathematical analysis shows that cognitive failure under stress is “not a bug — it is an inherent feature” of the cognition/regulation dyad. The distinction between structure regulation and perception regulation yields qualitatively different failure modes. Wallace warns that the full mathematical apparatus (“groupoid symmetry-breaking phase transitions”) has been deliberately pruned for accessibility: “The term is common in string theory, and this should be a warning: Here there be Tygers.” The engineering design and implementation of corrective measures “will require tools at the very outer boundaries of current formal theory. Yes, cognitive science really is even more challenging than cutting-edge physics, Tech Bro venture capital pitches to the contrary.”

28. 26

    Note 26. G. Nair, F. Fagnani, S. Zampieri, and R. Evans, “Feedback control under data rate constraints: an overview,” Proceedings of the IEEE 95 (2007): 108-138. The Data Rate Theorem establishes that controlling an inherently unstable system requires control information at a rate exceeding the system’s topological information generation (the rate at which the system creates new distinguishable states). Wallace applies this theorem to cognition: treated as an inherently unstable system, a mind needs regulatory information at least as fast as it generates new distinguishable states.

29. 27

    Note 27. The critical threshold ατ < exp[-1] ≈ 0.368 emerges from the delay differential equation governing cognitive dynamics under friction (α) and delay (τ). Beyond this threshold, solutions oscillate instead of settling smoothly, and under further friction or delay the oscillations grow until the system fails. (In the simplest linear delay equation, the oscillations begin to grow only at ατ = π/2 ≈ 1.57.) See Wallace (2026) and Bernard et al., “Sufficient conditions for stability of linear differential equations with distributed delay,” Discrete and Continuous Dynamical Systems B 1 (2001): 233-256.

30. 28

    Note 28. Wallace’s observation that AI without embodiment can “only express bizarre and hallucinatory dreams of reason” echoes Hubert Dreyfus’s critique in What Computers Can’t Do (1972), but now with mathematical grounding. In Wallace’s Rate Distortion Control Theory model, stable cognition requires embodiment: a thermodynamic argument for the conclusion Dreyfus reached philosophically.

31. 29

    Note 29. Richard E. Nisbett, Kaiping Peng, Incheol Choi, and Ara Norenzayan, “Culture and systems of thought: holistic vs. analytic cognition,” Psychological Review 108 (2001): 291-310. This paper established that cognitive processes themselves vary systematically across cultures — East Asians attend more to context and relationships (holistic), while Westerners focus more on salient objects and categories (analytic). The distinction is not about intelligence but about what aspects of a situation receive attention. [Inference] Wallace’s distinction between structure regulation and perception regulation may map onto this cultural dimension.

32. 30

    Note 30. Richard P. Feynman, Lectures on Computation (Westview Press, 2000), especially the chapter on “The Physics of Information.” Charles H. Bennett, “The thermodynamics of computation,” International Journal of Theoretical Physics 21 (1982): 905-940. Bennett’s imaginary machine that converts message information into useful work establishes that information is literally a form of free energy, not merely analogous to it.

33. 31

    Note 31. Maryanne Wolf, Proust and the Squid: The Story and Science of the Reading Brain (Harper Perennial, 2007) and Reader, Come Home: The Reading Brain in a Digital World (Harper, 2018). Wolf’s research demonstrates that the reading brain is constructed through practice, with different writing systems producing different neural architectures. Japanese readers develop two distinct circuits for kana and kanji; Chinese readers devote more right-hemisphere visual cortex to logographic processing than English readers do. Her principle, “what we do when we read makes a difference in the circuit itself,” extends to all media: the brain reflects the cognitive and perceptual requirements of its inputs.

34. 32

    Note 32. David Eagleman, “The Brain and The Now,” Long Now Foundation seminar (2016); see also Stetson, Fiesta, and Eagleman, “Does Time Really Slow Down during a Frightening Event?” PLoS ONE 2:12 (2007): e1295 (note 43). Eagleman’s research on temporal perception demonstrates that we live approximately half a second in the past — the brain collecting and synchronizing signals before constructing conscious experience. The flash-lag experiments show perception depends on events after the moment being perceived. His temporal recalibration experiments reveal that motor action serves as the brain’s synchronization mechanism; schizophrenic patients who fail to recalibrate show characteristic symptoms of credit misattribution. The duration dilation during fear is not actual slow-motion perception but retrospective inference from densified memory — time and memory are intertwined.

35. 35

    Note 35. The undecidability of Hilbert’s tenth problem was established by Matiyasevich, Y., “Enumerable sets are Diophantine,” Doklady Akademii Nauk SSSR 191 (1970): 279–282, building on work by Davis, Putnam, and Robinson. Its bearing on nonlinear dynamics is discussed in Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos (2003). Springer. The key insight is that sufficiently rich nonlinear dynamical systems can encode Diophantine equations, so some questions about their long-term behavior are formally undecidable.

36. 36

    Note 36. Wolfram, Stephen, A New Kind of Science (2002). Wolfram’s concept of computational irreducibility holds that many systems are such that no shortcut exists for predicting their behavior — the only way to determine the outcome is to run the computation step by step.

37. 37

    Note 37. DeSilva, J.M., et al., “When and Why Did Human Brains Decrease in Size? A New Change-Point Analysis,” Frontiers in Ecology and Evolution 9 (2021): 742639. Analysis of 985 fossil and modern crania identified a significant reduction in brain volume beginning approximately 3,000 years ago. The authors attribute the reduction to the externalization of knowledge in larger societies, through cities, writing, and institutional knowledge-sharing. A reassessment of the same data found no significant reduction in that window: Brian Villmoare and Mark Grabowski, “Did the transition to complex societies in the Holocene drive a reduction in brain size? A reassessment of the DeSilva et al. (2021) hypothesis,” Frontiers in Ecology and Evolution 10 (2022): 963568.

38. 38

    Note 38. Pearce, E., Stringer, C., and Dunbar, R.I.M., “New insights into differences in brain organization between Neanderthals and anatomically modern humans,” Proceedings of the Royal Society B 280 (2013): 20130168. Neanderthal endocranial volumes averaged larger than those of anatomically modern humans, but a greater proportion was devoted to visual processing and body maintenance, leaving less capacity for the social cognition that enabled Homo sapiens to build larger, more coordinated groups.

39. 39

    Note 39. Furness, J.B., “The enteric nervous system and neurogastroenterology,” Nature Reviews Gastroenterology & Hepatology 9 (2012): 286–294. Comprehensive review establishing that the enteric nervous system contains approximately 200–600 million neurons (comparable to the spinal cord), operates semi-autonomously from the central nervous system, and uses more than 30 neurotransmitters, most of which are identical to those found in the brain.

40. 40

    Note 40. Cassidy, S.B., et al., “Prader-Willi syndrome,” Genetics in Medicine 14 (2012): 10–26. Clinical review of the genetic, neurological, and endocrinological basis of Prader-Willi syndrome, including the disruption of hypothalamic satiety signaling that produces the characteristic insatiable hunger despite adequate nutrition.

41. 40b

    Note 40b. Chetan Prakash, Kyle D. Stephens, Donald D. Hoffman, Manish Singh, and Chris Fields, “Fitness Beats Truth in the Evolution of Perception,” Acta Biotheoretica 69 (2021): 319–341. See also Hoffman, D.D., The Case Against Reality: Why Evolution Hid the Truth from Our Eyes (W.W. Norton, 2019).

42. 41

    Note 41. Nichols, D.E., “Psychedelics,” Pharmacological Reviews 68 (2016): 264–355. Comprehensive pharmacological review of classical psychedelics, documenting the deep evolutionary conservation of the serotonin 2A receptor across vertebrate lineages, the independent evolution of structurally similar psychoactive alkaloids across fungi, plants, and animal venoms, and the receptor’s role in modulating cortical entropy and cognitive flexibility.

43. 42

    Note 42. See Raichle, M.E. and Gusnard, D.A., “Appraising the brain’s energy budget,” PNAS 99 (2002): 10237–10239, for the canonical measurement of brain metabolic costs.

44. 42e

    Note 42e. Roy, D.S., Park, Y.-G., Kim, M., Zhang, Y., Ogawa, S. et al., “Brain-wide mapping reveals that engrams for a single memory are distributed across multiple brain regions,” Nature Communications 13 (2022): 1799. DOI: 10.1038/s41467-022-29384-4. The Tonegawa laboratory mapped a single fear memory across 247 brain regions using fluorescent labeling of engrams (the physical traces a memory leaves in the brain) and SHIELD tissue clearing (developed by co-author Kwanghun Chung). Ranked 117 regions by “engram index.” Key findings: ~60% encoding-recall overlap; optogenetic reactivation of predicted regions induced memory recall; simultaneous multi-region reactivation produced superlinearly stronger recall; inhibiting CA1 (a hippocampal subfield) or BLA (the basolateral amygdala) reduced but did not eliminate downstream engram activity. Confirmed Richard Semon’s century-old prediction of a “unified engram complex.” The study provides the most comprehensive evidence that the mammalian brain distributes a single memory across a widely connected network. [Inference] That silencing CA1 or BLA weakened the downstream engram without abolishing it fits a picture in which participating regions coordinate by synaptic receptivity rather than central assignment.

45. 43

    Note 43. Stetson, Chess, Matthew P. Fiesta, and David M. Eagleman, “Does Time Really Slow Down during a Frightening Event?” PLoS ONE 2(12) (2007): e1295. Subjects overestimated fall duration by 36%, despite no change in temporal resolution during the fall itself.

46. 44

    Note 44. See Eagleman, David, Incognito: The Secret Lives of the Brain (2011), for the neural conduction delay experiments demonstrating that taller individuals experience a measurably longer lag between stimulus and conscious perception.

47. 45

    Note 45. Hofstadter, Douglas R., Gödel, Escher, Bach: An Eternal Golden Braid (Basic Books, 1979), p. 612. Hofstadter relays Crick’s observation about the fundamental constraint on self-reproducing systems: the information-bearing function (DNA) and the catalytic function (proteins) cannot be efficiently combined in a single molecule.

48. 46

    Note 46. Carelli, P.V. et al., “Whole-Brain Empirical Analysis of Criticality versus Synchronization,” Physical Review Letters 122 (2019): 248101. The team satisfied the Sethna exponent-relation test (the most stringent available criterion for criticality) and found a universal size-duration scaling ratio across rats, mice, monkeys, and turtles. See also Fontenele, A.J. et al., “Criticality between Cortical States,” Physical Review Letters 122 (2019): 208101, for the three-exponent relationship in rat cortex.

49. 46a

    Note 46a. Gustavo Deco, Yonatan Sanz Perl, and Morten L. Kringelbach, “Complex harmonics reveal low-dimensional manifolds of critical brain dynamics,” Physical Review E 111 (2025): 014410.

50. 48

    Note 48. Gidon, A., Zolnik, T.A., Fidzinski, P., Bolduan, F., Papoutsi, A., Poirazi, P., Holtkamp, M., Vida, I., and Larkum, M.E., “Dendritic action potentials and computation in human layer 2/3 cortical neurons,” Science 367(6473) (2020): 83–87. The study identified a novel class of calcium-mediated dendritic action potentials in human cortical neurons, with graded activation enabling XOR-like computation within individual dendritic compartments. Minsky and Papert’s XOR impossibility proof: Perceptrons (MIT Press, 1969). For the two-layer neuron model that preceded this work: Poirazi, P., Brannon, T., and Mel, B.W., “Pyramidal neuron as two-layer neural network,” Neuron 37(6) (2003): 989–999.

51. 49

    Note 49. Gillis, J.A. et al., “The transcriptional legacy of developmental stochasticity,” bioRxiv 2019.12.11.873265 (2019). Nine-banded armadillos produce litters of genetically identical quadruplets; the study found that random X-inactivation patterns at the ~25-cell stage and autosomal expression ratios fixed at the ~200-cell stage create permanent, individually unique gene expression signatures. Approximately 10% of total variation among siblings was attributable to developmental noise. See also Mitchell, K., Innate: How the Wiring of Our Brains Shapes Who We Are (Princeton University Press, 2018), for the broader argument that developmental noise constitutes a third major source of phenotypic variation alongside genes and environment.

52. 50

    Note 50. Linneweber, G.A. et al., “A neurodevelopmental origin of behavioral individuality in the Drosophila visual system,” Science 367(6482) (2020): 1112–1119. Senior author: Bassem A. Hassan (Paris Brain Institute). The study causally linked random asymmetries in dorsal cluster neuron wiring to individual differences in walking behavior among genetically identical flies; manipulating asymmetry directly altered navigational efficiency.

53. dec

    Note dec. Shinbrot, T. and Young, W., “Why decussate? Topological constraints on 3D wiring,” The Anatomical Record 291(10) (2008): 1278–1292; also available on arXiv: 2405.07837. The paper showed that for any system where a central controller interacts with a 3D environment, uncrossed wiring creates geometric singularities confounding spatial axes. They proved a critical threshold: systems with more than roughly 100–500 neurons (depending on targeting error rates) are unstable under ipsilateral wiring (same-side connections) but stable under contralateral wiring (crossed connections). The crossed configuration is the only one that scales, and the crossing itself is conserved from nematodes to humans. See also R. Douglas Fields, “Why the Brain’s Connections to the Body Are Crisscrossed,” Quanta Magazine (19 April 2023) for an accessible treatment.

54. 51

    Note 51. Abdo, H. et al., “Specialized cutaneous Schwann cells initiate pain sensation,” Science 365(6454) (2019): 695–699. The study identified a previously unknown type of glial cell forming a mesh-like organ in the skin’s subepidermal border, required for mechanical pain sensation. Optogenetic activation of the glial cells alone (without direct neuronal stimulation) produced pain behaviors in mice.

55. 43a

    Note 43a. Payeur, A., Guerguiev, J., Zenke, F., Richards, B.A., and Naud, R., “Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits,” Nature Neuroscience 24 (2021): 1010–1019. Proposes that neuron bursts function as a biologically plausible teaching signal, approximating backpropagation without pausing sensory processing. The model requires two-compartment neurons where apical dendrites listen for burst-encoded correction signals while basal dendrites relay sensory information — dual processing streams that pass each other simultaneously. See also Whitten, A., “Neuron Bursts Can Mimic Famous AI Learning Strategy,” Quanta Magazine (18 October 2021).

56. ruffini-kt

    Note ruffini-kt. Giulio Ruffini, “An algorithmic information theory of consciousness,” Neuroscience of Consciousness 2017(1): nix019 (2017). The Kolmogorov Theory (KT) proposes that structured experience arises from compressive models of input-output streams. KT bridges IIT, global workspace theory, and predictive processing via a single mechanism: algorithmic compression. KT brackets the hard problem (“we assume there is consciousness”) and focuses on what structures experience, as does this book’s preference-sufficiency framework.

KT’s experimental predictions extend beyond PCI. Several paradigms from the paper warrant future development:

Binocular rivalry and model selection. When two different images are presented to each eye, the brain selects the simplest available model: subjects see one image, not both. KT predicts that the dominant image will be the one requiring less algorithmic complexity to model (consistent with available priors). Natural images dominate over artificial ones (Daniel H. Baker and Erich W. Graf, “Natural images dominate in binocular rivalry,” PNAS 106 (2009): 5436-5441), recognizable figures dominate over unrecognizable patterns of similar complexity (Karen Yu and Randolph Blake, “Do recognizable figures enjoy an advantage in binocular rivalry?” Journal of Experimental Psychology: Human Perception and Performance 18 (1992): 1158-1173), and images consistent with ongoing VR experience dominate over inconsistent ones. The prediction: the brain chooses the model that compresses the most data most succinctly, and the chosen model is what the subject experiences.

Presence as compression. Virtual reality Presence (the subjective experience of “being there”) maps onto KT’s framework: Presence strengthens when sensorimotor data are consistent with a single low-complexity model. A VR environment with coherent physics, consistent visual-proprioceptive coupling, and plausible object behavior is compressible. One with physics glitches, tracking lag, or visual-vestibular mismatch is not. KT predicts Presence intensity is inversely proportional to the algorithmic complexity of the best available model of the current sensory stream.

Oddball paradigms and compression detection. The mismatch negativity (MMN) and P300b ERP components signal rule-breaking in auditory or visual sequences. Under KT, these are signatures of compression failure: the brain’s running model predicted one pattern; reality delivered another. The prediction error itself is informative. KT predicts that oddball responses should weaken and slow as the violated rule’s algorithmic complexity rises: simple rules (AABAABAAB…) broken by a deviant (AABAABAAC) should produce faster, stronger responses than complex rules (patterns requiring longer programs to specify). Experiments with sequences of systematically increasing Kolmogorov complexity could map the brain’s compression capacity as a function of conscious state, pharmacological intervention, or developmental stage.

1. ruffini-casali

   Note ruffini-casali. Adenauer G. Casali et al., “A theoretically based index of consciousness independent of sensory processing and behavior,” Science Translational Medicine 5(198): 198ra105 (2013). The Perturbational Complexity Index (PCI) compresses TMS-evoked EEG responses using Lempel-Ziv-Welch (LZW). Conscious states produce PCI values between 0.31 and 0.70; unconscious states fall below 0.31. The measure discriminates across wakefulness, REM sleep, NREM sleep, ketamine sedation, propofol anesthesia, minimally conscious state, vegetative state, and locked-in syndrome. Ruffini’s KT reinterprets PCI: high PCI reflects deep computation (a compressive model generating apparently complex output), not merely high integration. The distinction matters for Becoming Minds: a system could have high PCI-equivalent measures (complex, structured responses to perturbation) without biological integration in Tononi’s sense.