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Emergence of Brains

William Bialek

PRX Life 3, 037002 – Published 7 August, 2025

DOI: https://doi.org/10.1103/62p9-wn32

Abstract

As with many creative human activities, physics resists definition. Physics, as the saying goes, is what physicists do. But we can recognize major themes. One theme is the reductionist search for the building blocks of matter. In another direction is the exploration of the origins and history of the universe writ large. At intermediate scales, we explore the emergence of macroscopic behaviors that are more than the sum of their parts. An important lesson of the late 20th century is that these seemingly distinct themes are intertwined, so that theoretical physics today is more unified while at the same time reaching ambitiously across an even broader range of topics. The 2024 Nobel Prize in Physics, awarded jointly to John Hopfield and Geoffrey Hinton, celebrates the discovery of new classes of emergent phenomena, inspired by the function of brains and minds.

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References (100)

  1. The Nobel Committee for Physics, Royal Swedish Academy of Sciences, Scientific background to the Nobel Prize in Physics (2024), https://www.nobelprize.org/prizes/physics/2024/advanced-information/.
  2. J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
  3. P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin/Cummings, Menlo Park, CA, 1984).
  4. J. P. Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity (Oxford University, Oxford, 2021).
  5. S. A. Kivelson, J. M. Jiang, and J. Chang, Statistical Mechanics of Phases and Phase Transitions (Princeton University, Princeton, NJ, 2024).
  6. M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
  7. B. G. Cragg and H. N. V. Temperley, The organisation of neurones: A co-operative analogy, Electroencephalogr. Clin. Neurophysiol. 6, 85 (1954).
  8. L. N. Cooper, A possible organization of animal memory and learning, in Collective Properties of Physical Systems: Proceedings of Nobel Symposium, edited by B. Lundqvist and S. Lundqvist (Academic Press, New York, 1973), pp. 252–264.
  9. W. A. Little, Existence of persistent states in the brain, Math. Biosci. 19, 101 (1974).
  10. W. A. Little and G. L. Shaw, Analytic study of the memory storage capacity of a neural network, Math. Biosci. 39, 281 (1978).
  11. T. Kohonen, Correlation matrix memories, IEEE Trans. Comput. C-21, 353 (1972).
  12. S. I. Amari, Learning patterns and pattern sequences by self-organizing nets of threshold elements, IEEE Trans. Comput. C-21, 1197 (1972).
  13. S. I. Amari, Neural theory of association and concept-formation, Biol. Cybern. 26, 175 (1977).
  14. W. Bialek, Moving boundaries: An appreciation of John Hopfield, arXiv:2412.18030.
  15. R. G. Shulman, S. Ogawa, and J. J. Hopfield, An allosteric model of hemoglobin: II. The assumption of independent binding, Arch. Biochem. Biophys. 151, 68 (1972).
  16. J. J. Hopfield, Relation between structure, co-operativity and spectra in a model of hemoglobin action, J. Mol. Biol. 77, 207 (1973).
  17. J. J. Hopfield, Electron transfer between biological molecules by thermally activated tunneling, Proc. Natl. Acad. Sci. USA 71, 3640 (1974).
  18. J. J. Hopfield, Kinetic proofreading: A new mechanism for reducing errors in biosynthetic processes requiring high specificity, Proc. Natl. Acad. Sci. USA 71, 4135 (1974).
  19. J. Ninio, Kinetic amplification of enzyme discrimination, Biochimie 57, 587 (1975).
  20. C. H. Bennett, The thermodynamics of computation—A review, Int. J. Theor. Phys. 21, 905 (1982).
  21. L. Peliti and S. Pigolotti, Stochastic Thermodynamics: An Introduction (Princeton University, Princeton, NJ, 2021).
  22. H. S. Seung, How the brain keeps the eyes still, Proc. Natl. Acad. Sci. USA 93, 13339 (1996).
  23. G. Major, R. Baker, E. Aksay, B. Mensh, H. S. Seung, and D. W. Tank, Plasticity and tuning by visual feedback of the stability of a neural integrator, Proc. Natl. Acad. Sci. USA 101, 7739 (2004).
  24. G. Major, R. Baker, E. Aksay, H. S. Seung, and D. W. Tank, Plasticity and tuning of the time course of analog persistent firing in a neural integrator, Proc. Natl. Acad. Sci. USA 101, 7745 (2004).
  25. J. J. Hopfield and D. W. Tank, “Neural” computation of decisions in optimization problems, Biol. Cybern. 52, 141 (1985).
  26. J. J. Hopfield and D. W. Tank, Computing with neural circuits: A model, Science 233, 625 (1986).
  27. D. W. Tank and J. J. Hopfield, Collective computation in neuron-like circuits, Sci. Am. 257, 104 (1987).
  28. S. Kirkpatrick, C. D. Gelatt, Jr., and M. Vecchi, Optimization by simulated annealing, Science 220, 671 (1983).
  29. Y. Fu and P. W. Anderson, Application of statistical mechanics to NP-complete problems in combinatorial optimisation, J. Phys. A: Math. Gen. 19, 1605 (1986).
  30. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky, Determining computational complexity from characteristic ‘phase transitions', Nature (London) 400, 133 (1999).
  31. E. Gardner, The space of interactions in neural network models, J. Phys. A: Math. Gen. 21, 257 (1988).
  32. E. Levin, N. Tishby, and S. A. Solla, A statistical approach to learning and generalization in layered neural networks. Proc. IEEE 78, 1568 (1990).
  33. E. Gardner, Multiconnected neural network models, J. Physi. A: Math. Gen. 20, 3453 (1987).
  34. D. H. Ackley, G. E. Hinton, and T. J. Sejnowski, A learning algorithm for Boltzmann machines, Cognit. Sci. 9, 147 (1985).
  35. P. Smolensky, Information processing in dynamical systems: Foundations of harmony theory, in Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol. 1: Foundations, edited by D. E. Rumelhart and J. L. McClelland (MIT, Cambridge MA, 1986), pp. 194–281.
  36. G. Hinton, Boltzmann machines, Nobel Prize Lecture, 2024, https://www.nobelprize.org/prizes/physics/2024/hinton/lecture/.
  37. H. D. Block, The perceptron: A model for brain functioning. I, Rev. Mod. Phys. 34, 123 (1962).
  38. H. D. Block, B. W. Knight, Jr., and F. Rosenblatt, Analysis of a four-layer series-coupled perceptron. II, Rev. Mod. Phys. 34, 135 (1962).
  39. Y. LeCun, Y. Bengio, and G. Hinton, Deep learning, Nature (London) 521, 436 (2015).
  40. G. E. Hinton, S. Osindero, and Y. W. Teh, A fast learning algorithm for deep belief nets, Neural Comput. 18, 1527 (2006).
  41. A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, I. Polosukhin, Attention is all you need, Adv. Neural Inf. Process. Syst. 30, 5999 (2017).
  42. D. Krotov and J. J. Hopfield, Dense associative memory for pattern recognition, Adv. Neural Inf. Process. Syst. 29, 1180 (2016).
  43. H. Ramsauer, B Schäfl, J. Lehner, P. Seidl, M. Widrich, T. Adler, L. Gruber, M. Holzleitner, M. Pavlović, G. K. Sandve, V. Greiff, D. Kreil, M. Kopp, G. Klambauer, J. Brandstetter, and S. Hochreiter, Hopfield networks is all you need, arXiv:2008.02217.
  44. W. Bialek, Biophysics: Searching for Principles (Princeton University, Princeton, NJ, 2012).
  45. W. Bialek, B. Carragher, I. Cissé, M. M. Desai, O. K. Dudko, D. I. Goldman, J. Kondev, P. B. Littlewood, A. J. Liu, M. E. Moxon, J. N. Onuchic, M. J. Schnitzer, and C. M. Waterman, Physics of Life: A Consensus Study (National Academies, Washington, DC, 2022).
  46. From Statistical Physics to Statistical Inference and Back, edited by P. Grassberger and J. P. Nadal (Kluwer Academic, Dordrecht, 1994).
  47. J. J. Hopfield, Physics is a point of view. Nobel Prize Lecture, 2024, https://www.nobelprize.org/prizes/physics/2024/hopfield/lecture/.
  48. J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A. Židek, A. Potapenko, A. Bridgland, C. Meyer, S. A. A. Kohl, A. J. Ballard, A. Cowie, B. Romera-Paredes, S. Nikolov, R. Jain, J. Adler, T. Back et al., Highly accurate protein structure prediction with AlphaFold, Nature (London) 596, 583 (2021).
  49. R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  50. V. Acquaviva, Machine Learning for Physics and Astronomy (Princeton University, Princeton, 2023).
  51. S. R. Datta, D. J. Anderson, K. Branson, P. Perona, and A. Leifer, Computational neuroethology: A call to action, Neuron 104, 11 (2019).
  52. C. A. Riiska, C. Nguyen, O. Peleg, and J. M. Rieser, The physics of animal behavior: Form, function, and interactions, Ann. Rev. Condens. Matter Phys. 15, 325 (2024).
  53. A. Mathis, P. Mamidanna, K. M. Cury, T. Abe, V. N. Murthy, M. W. Mathis, and M. Bethge, DeepLabCut: Markerless pose estimation of user-defined body parts with deep learning, Nat. Neurosci. 21, 1281 (2018).
  54. T. D. Pereira, D. E. Aldarondo, L. Willmore, M. Kislin, S. S.-H. Wang, M. Murthy, and J. W. Shaevitz, Fast animal pose estimation using deep neural networks, Nat. Methods 16, 117 (2019).
  55. T. D. Pereira, N. Tabris, A. Matsliah, D. M. Turner, J. Li, S. Ravindranath, E. S. Papadoyannis, E. Normand, D. S. Deutsch, Z. Y. Wang, G. C. McKenzie-Smith, C. C. Mitelut, M. D. Castro, J. D'Uva, M. Kislin, D. H. Sanes, S. D. Kocher, S. S.-H. Wang, A. L. Falkner, J. W. Shaevitz et al., SLEAP: A deep learning system for multi-animal pose tracking, Nat. Methods 19, 486 (2022).
  56. T. Ahamed, A. C. Costa, and G. J. Stephens, Capturing the continuous complexity of behaviour in Caenorhabditis elegans, Nat. Phys. 17, 275 (2021).
  57. B. C. Daniels and I. Nemenman, Automated adaptive inference of phenomenological dynamical models, Nat. Commun. 6, 8133 (2015).
  58. B. C. Daniels, W. S. Ryu, and I. Nemenman, Automated, predictive, and interpretable inference of Caenorhabditis elegans escape dynamics, Proc. Natl. Acad. Sci. USA 116, 7226 (2019).
  59. J. Kaplan, S. McCandlish, T. Henighan, T. B. Brown, B. Chess, R. Child, S. Gray, A. Radford, J. Wu, and D. Amodei, Scaling laws for neural language models, arXiv:2001.08361.
  60. T. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell, S. Agarwal, A. Herbert-Voss, G. Krueger, T. Henighan, R. Child, A. Ramesh, D. Ziegler, J. Wu, C. Winter, C. Hesse et al., Language models are few-shot learners, Adv. Neural Inf. Process. Syst. 33, 1877 (2020).
  61. P. Mehta, M. Bukov, C. H. Wang, A. G. R. Day, C. Richardson, C. K. Fisher, and D. J. Schwab, A high-bias, low-variance introduction to machine learning for physicists, Phys. Rep. 810, 1 (2019).
  62. G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborová, Machine learning and the physical sciences, Rev. Mod. Phys. 91, 045002 (2019).
  63. Y. Bahri, J. Kadmon, J. Pennington, S. S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annu. Rev. Condens. Matter Phys. 11, 501 (2020).
  64. Y. Feng and Y. Tu, The inverse variance–flatness relation in stochastic gradient descent is critical for finding flat minima, Proc. Natl. Acad. Sci. USA 118, e2015617118 (2021).
  65. F. Mignacco and P. Urbani, The effective noise of stochastic gradient descent, J. Stat. Mech. 2022, 083405 (2022).
  66. A. Sclocchi and M. Wyart, On the different regimes of stochastic gradient descent, Proc. Natl. Acad. Sci. USA 121, e2316301121 (2024).
  67. L. Tiberi, F. Mignacco, K. Irie, and H. Sompolinsky, Dissecting the interplay of attention paths in a statistical mechanics theory of transformers, arXiv:2405.15926.
  68. S. Goldt, M. Mézard, F. Krzakala, and L. Zdeborová, Modeling the influence of data structure on learning in neural networks: The hidden manifold model, Phys. Rev. X 10, 041044 (2020).
  69. J. Garnier-Brun, M. Mézard, E. Moscato, and L. Saglietti, How transformers learn structured data: Insights from hierarchical filtering, arXiv:2408.15138.
  70. A. Nguyen, D. J. Schwab, and V. Ngampruetikorn, Generalization vs. specialization under concept shift, arXiv:2409.15582.
  71. M. Kamb and S. Ganguli, An analytic theory of creativity in convolutional diffusion models, arXiv:2412.20292.
  72. A. Sclocchi, A. Favero, and M. Wyart, A phase transition in diffusion models reveals the hierarchical nature of data, Proc. Natl. Acad. Sci. USA 122, e2408799121 (2025).
  73. M. Stern and A. Murugan, Learning without neurons in physical systems, Ann. Rev. Condens. Matter Phys. 14, 417 (2023).
  74. C. Goddard, L. M. Smith, V. Ngampruetikorn, and D. J. Schwab, When can in-context learning generalize out of task distribution? arXiv:2506.05574.
  75. D. J. Amit, Modeling Brain Function: The World of Attractor Neural Networks (Cambridge University, Cambridge, England, 1989).
  76. A. Treves, O. Miglino, and D. Parisi, Rats, nets, maps, and the emergence of place cells, Psychobiology 20, 1 (1992).
  77. K. J. Yoon, M. A. Buice, C. Barry, R. Hayman, N. Burgess, and I. R. Fiete, Specific evidence of low-dimensional continuous attractor dynamics in grid cells, Nat. Neurosci. 16, 1077 (2013).
  78. J. D. Seelig and V. Jayaraman, Neural dynamics for landmark orientation and angular path integration, Nature (London) 521, 186 (2015).
  79. S. S. Kim, H. Rouault, S. Druckmann, and V. Jayaraman, Ring attractor dynamics in the Drosophila central brain, Science 356, 849 (2017).
  80. D. L. K. Yamins and J. J. DiCarlo, Nat. Neurosci. 19, 356 (2016).
  81. N. Maheswaranathan, L. T. McIntosh, H. Tanaka, S. Grant, D. B. Kastner, J. B. Melander, A. Nayebi, L. E. Brezovec, J. H. Wang, S. Ganguli, and S. A. Baccus, Interpreting the retinal neural code for natural scenes: From computations to neurons, Neuron 111, 2742.E4 (2023).
  82. L. Meshulam and W. Bialek, Statistical mechanics for networks of real neurons, arXiv:2409.00412 [Rev. Mod. Phys. (to be published)].
  83. S. F. Taylor, N. Tishby, and W. Bialek, Information and fitness, arXiv:0712.4382.
  84. D. D. Martino, F. Capuani, and A. D. Martino, Growth against entropy in bacterial metabolism: The phenotypic trade-off behind empirical growth rate distributions in E. coli, Phys. Biol. 13, 036005 (2016).
  85. D. De Martino, A. M. Andersson, T. Bergmiller, C. C. Guet, and G. Tkačik, Statistical mechanics for metabolic networks during steady state growth, Nat. Commun. 9, 2988 (2018).
  86. N. H. Barton and H. P. de Vladar, Statistical mechanics and the evolution of polygenic quantitative traits, Genetics 181, 997 (2009).
  87. K. Bod'ová, G. Tkačik, and N. H. Barton, A general approximation for the dynamics of quantitative traits, Genetics 202, 1523 (2016).
  88. W. Młynarski, M. Hledák, T. R. Sokolowski, and G. Tkačik, Statistical analysis and optimality of neural systems, Neuron 109, P1227.E5 (2021).
  89. M. Carneiro and D. L. Hartl, Adaptive landscapes and protein evolution, Proc. Natl. Acad. Sci. USA 107, 1747 (2010).
  90. A. Papkou, L. Garcia-Pastor, J. Escudero, and A. Wagner, A rugged yet easily navigable fitness landscape, Science 382, eadh3860 (2023).
  91. R. D. Peccei and H. R. Quinn, CP conservation in the presence of pseudoparticles, Phys. Rev. Lett. 38, 1440 (1977).
  92. S. Weinberg, A new light boson? Phys. Rev. Lett. 40, 223 (1978).
  93. F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  94. L. F. Abbott, A mechanism for reducing the value of the cosmological constant, Phys. Lett. B 150, 427 (1985).
  95. P. J. Steinhardt and N. Turok, Why the cosmological constant is small and positive, Science 312, 1180 (2006).
  96. G. LeMasson, E. Marder, and L. F. Abbott, Activity-dependent regulation of conductances in model neurons, Science 259, 1915 (1993).
  97. G. Turrigiano, L. F. Abbott, and E. Marder, Activity-dependent changes in the intrinsic properties of cultured neurons, Science 264, 974 (1994).
  98. J. N. Onuchic, Z. Luthey-Schulten, and P. G. Wolynes, Theory of protein folding: The energy landscape perspective, Annu. Rev. Phys. Chem. 48, 545 (1997).
  99. H. Li, C. Tang, and N. S. Wingreen, Are protein folds atypical? Proc. Natl. Acad. Sci. USA 95, 4987 (1998).
  100. M. Bauer, W. Bialek, C. Goddard, C. M. Holmes, K. Krishnamurthy, S. E. Palmer, R. Pang, D. J. Schwab, and L. Susman, Optimization and variability can coexist, arXiv:2505.23398.

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