Invariances in Theory

  • Mario NegrelloEmail author
Part of the Springer Series in Cognitive and Neural Systems book series (SSCNS, volume 1)


This chapter surveys the multifaceted roles that invariants play in theorizing, from physics and mathematics to biology and neurobiology. The question “What is an invariant of behavior?” is posed, and some alternatives are proposed and discussed: genes, neuroanatomy, and reflex theory. From that, the cybernetic take on the issue is introduced and placed in an evolutionary context, in which single behaviors are identified in respect to the goals they achieve and how they subserve the organism’s viability. The search for invariants of behavior is framed as a search for mechanisms. This search is far from trivial, as assumptions play a prominent role.


Component Function Functional Behavior Behavioral Function Simple Organism Developmental System Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Arbib MA (1972) The metaphorical brain, an introduction to cybernetics and brain theory. MIT Press, CambridgeGoogle Scholar
  2. 2.
    Arbib MA (1982) Machine Intelligence 10, Chichester: Ellis Horwood, chap Rana Computatrix, an evolving model of visuomotor coordination in frog and toad, pp 501–517Google Scholar
  3. 3.
    Arbib MA, Fellous JM (2004) Emotions: From brain to robot. Trends Cogn Sci 8(12)Google Scholar
  4. 4.
    Ashby W (1960) Design for a brain: The origin of adaptive behavior, 2nd edn. Chapman & Hall, LondonCrossRefGoogle Scholar
  5. 5.
    Bateson G (1972) Steps to an ecology of mind. University of Chicago Press, p. 533Google Scholar
  6. 6.
    Benavides-Piccione R, Hamzei-Sichani F, Ballesteros-Yanez I, DeFelipe J, Yuste R (2006) Dendritic size of pyramidal neurons differs among mouse cortical regions. Cereb Cortex 16(7):990–1001PubMedCrossRefGoogle Scholar
  7. 7.
    Berns GS, Sejnowski TJ (1998) A computational model of how the basal ganglia produce sequences. J Cogn Neurosci 10(1):108–121PubMedCrossRefGoogle Scholar
  8. 8.
    Braitenberg V (1977) On the texture of brains: An introduction to neuroanatomy for the cybernetically minded. Springer, New YorkGoogle Scholar
  9. 9.
    Braitenberg V (1984) Vehicles, experiments in synthetic psychology. Bradford Book, CambridgeGoogle Scholar
  10. 10.
    Braitenberg V (2001) Brain size and number of neurons: An exercise in synthetic neuroanatomy. J. Comput. Neurosci. 10(1):71–77PubMedCrossRefGoogle Scholar
  11. 11.
    Braitenberg V, Schüz A (1998) Cortex: Statistics and geometry of neuronal connectivity. Springer, BerlinGoogle Scholar
  12. 12.
    Brentano FC (1874) Psychologie vom empirischen Standpunkte. Duncker & Humblot, LeipzigGoogle Scholar
  13. 13.
    Cohen N, Squire L (1980) Preserved learning and retention of pattern-analyzing skill in amnesia: dissociation of knowing how and knowing that. Science 210(4466):207PubMedCrossRefGoogle Scholar
  14. 14.
    Dawkins R (1976) The selfish gene. Oxford University Press, New YorkGoogle Scholar
  15. 15.
    Di Paolo E (2002) Book review: Cycles of contingency. Artif Life 8(2)Google Scholar
  16. 16.
    Dörner D (1999) Bauplan für eine Seele. Rowohlt, ReinbekGoogle Scholar
  17. 17.
    Edelman G (1988) Topobiology: An introduction to molecular embryology. Basic BooksGoogle Scholar
  18. 18.
    Eigen M, Schuster P (1978) The hypercycle. Naturwissenschaften 65(1):7–41CrossRefGoogle Scholar
  19. 19.
    Elston G, Rockland K (2002) The pyramidal cell of the sensorimotor cortex of the Macaque Monkey: Phenotypic variation. Cereb Cortex 12(10):1071–1078PubMedCrossRefGoogle Scholar
  20. 20.
    Elston GN (2005) Cortex, cognition and the cell: New insights into the pyramidal neuron and prefrontal function. Cereb Cortex 13(11):1124–1238CrossRefGoogle Scholar
  21. 21.
    von Foerster H, von Glaserfeld E (2005) Einführung in den Konstruktivismus, 9th edn. Piper Press, MunichGoogle Scholar
  22. 22.
    Fox Keller E, Harel D (2007) Beyond the Gene. PLoS ONE 2(11):e1231CrossRefGoogle Scholar
  23. 23.
    Glaserfeld Ev (1990) Teleology and the concepts of causation. Philosophica 46(2):17–42Google Scholar
  24. 24.
    Goodwin B (2001) The evolution of complexity: How the leopard changed its spots. Princeton Academic, PrincetonGoogle Scholar
  25. 25.
    Goodwin B, Briere C (1989) A mathematical model of cytoskeletal dynamics and morphogenesis in acetabularia. The Cytoskeleton of the Algae. CRC Press, Boca Raton, pp 219–238Google Scholar
  26. 26.
    Gould SJ, Lewontin RD (1979) The spandrels of San Marcos and the Panglossian paradigm: A critic of the adaptationist programme. Proc R Soc Lond 205:581–598PubMedCrossRefGoogle Scholar
  27. 27.
    Griffiths PE, Gray RD (2000) Darwinism and developmental systems. MIT Press, CambridgeGoogle Scholar
  28. 28.
    Griffiths PE, Stoltz K (2007) The cambridge companion to the philosophy of biology. chap Gene, Cambridge University Press, Cambridge, pp 103–119Google Scholar
  29. 29.
    Hanlon R (2007) Cephalopod dynamic camouflage. Curr Biol 17(11):400–404CrossRefGoogle Scholar
  30. 30.
    Heylighen F, Joslyn C (2001) Cybernetics and second-order cybernetics. In: Meyers R (ed) Encyclopedia of Physical Science and Technology, 3rd edn. Academic, New YorkGoogle Scholar
  31. 31.
    von Holst VE, Mittelstaedt H (1950) Das Reafferenzprinzip. Die Naturwiss 37(20):464–476CrossRefGoogle Scholar
  32. 32.
    Homberg U, Paech A (2002) Ultrastructure and orientation of ommatidia in the dorsal rim area of the locust compound eye. Arthropod Struct Dev 30(4):271–280PubMedCrossRefGoogle Scholar
  33. 33.
    Jablonka E, Lamb M (2005) Evolution in four dimensions: Genetic, epigenetic, behavioral, and symbolic variation in the history of life. MIT Press, CambridgeGoogle Scholar
  34. 34.
    Jablonka E, Lamb M, Avital E (1998) ‘lamarckian’ mechanisms in darwinian evolution. Trends Ecol Evol 13(5):206–210PubMedCrossRefGoogle Scholar
  35. 35.
    Jewell E, Abate F, McKean E (2001) The new Oxford American dictionary. Oxford University Press, OxfordGoogle Scholar
  36. 36.
    Jonas H (2001 (1966)) The phenomenon of life. Northwestern University Press, Evanston, ILGoogle Scholar
  37. 37.
    Kauffman S (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 22(3):437–67PubMedCrossRefGoogle Scholar
  38. 38.
    Mayr E (1961) Cause and Effect in Biology Kinds of causes, predictability, and teleology are viewed by a practicing biologist. Science 134(3489):1501–1506PubMedCrossRefGoogle Scholar
  39. 39.
    Mayr E (1976) Evolution and the diversity of life. Harvard University Press, CambridgeGoogle Scholar
  40. 40.
    Merleau-Ponty M (1963 (translation), 1942) The Structure of Behavior. Duquesne University Press, PhiladelphiaGoogle Scholar
  41. 41.
    Minksy M (1975) The psychology of computer vision, chap A Framework for representing knowledge. McGraw-Hill, New YorkGoogle Scholar
  42. 42.
    Nagel E (1979) The structure of science: Problems in the logic of scientific explanation. Hackett Publishing, USAGoogle Scholar
  43. 43.
    Niven J (2008) Evolution: Convergent eye losses in fishy circumstances. Curr Biol 18(1):27–29CrossRefGoogle Scholar
  44. 44.
    Noether E (1918) Invariante variationsprobleme. Gott Nachr 235Google Scholar
  45. 45.
    Noether E, Tavel M (2005) Invariant variation problems. Arxiv preprint physics/0503066Google Scholar
  46. 46.
    O’Keefe J, Dostrovsky J (1971) The hippocampus as spatial map: preliminary evidence from unit activity in the freely moving rat. Brain Res 34:171–175PubMedCrossRefGoogle Scholar
  47. 47.
    Oyama S (2000) The ontogeny of information: Developmental systems and evolution. Duke University Press, DurhamGoogle Scholar
  48. 48.
    Oztop E, Kawato M, Arbib M (2006) Mirror neurons and imitation: A computationally guided review. Neural Netw 19(3):254–271PubMedCrossRefGoogle Scholar
  49. 49.
    Pais A (1982) Subtle is the Lord. The science and the life of A. Einstein. Oxford University Press, OxfordGoogle Scholar
  50. 50.
    Porter J, Baker R (1997) Absence of oculomotor and trochlear motoneurons leads to altered extraocular muscle development in the Wnt-1 null mutant mouse. Dev Brain Res 100(1): 121–126CrossRefGoogle Scholar
  51. 51.
    Quiroga R, Reddy L, Kreiman G, Koch C, Fried I (2005) Invariant visual representation by single neurons in the human brain. Nature 435(7045):1102–1107PubMedCrossRefGoogle Scholar
  52. 52.
    Rosenblueth A, Wiener N, Bigelow J (1943) Behavior, purpose and teleology. Philos Sci 10: 18–24CrossRefGoogle Scholar
  53. 53.
    Ryan L, Cox C, Hayes SM, Nadel L (2008) Hippocampal activation during episodic and semantic memory retrieval: Comparing category production and category cued recall. Neuropsychologia 46(8):2109–2121, DOI, URL
  54. 54.
    Smith JM, Burrian R, Kauffmann S, Alberch P, Campbell J, Goodwin B, Lande L, Raul D, Wolpert L (1985) Developmental constraints and evolution. Q Rev Biol 60(3):265–287CrossRefGoogle Scholar
  55. 55.
    Smith PG (2007) The cambridge companion to the philosophy of biology. Cambridge University Press, Cambridge, chap Information in Biology, pp 103–119Google Scholar
  56. 56.
    Sterelny K (2005) Thought in a hostile world. MIT Press, CambridgeGoogle Scholar
  57. 57.
    Swammerdam J (1737) Biblia Naturae, Sive Historia Insecto, vol 1. IDC (Leiden)Google Scholar
  58. 58.
    Ton R, Hackett J (1984) Neural mechanisms of startle behavior, Springer, Berlin, chap The Role of the Mauthner Cell in fast starts involving escape in Teleost FishesGoogle Scholar
  59. 59.
    Tracy A, Jarrard L, Davidson T (2001) The hippocampus and motivation revisited: appetite and activity. Behav Brain Res 127(1–2):13–23PubMedCrossRefGoogle Scholar
  60. 60.
    Turchin VF (1977) The Phenomenon of Science: a cybernetic approach to human evolution. Electronic URL
  61. 61.
    Varela F (1979) Principles of biological autonomy. North Holland, New YorkGoogle Scholar
  62. 62.
    Varela F, Maturana H (1987, 1998) The tree of knowledge, 1st edn. Shambala, Boston, MAGoogle Scholar
  63. 63.
    Varela F, Maturana H, Uribe R (1974) Autopoiesis: the organization of living systems, its characterization and a model. Curr Model Biol 5(4):187–96Google Scholar
  64. 64.
    Wiener N (1961) Cybernetics: or the control and communication in the animal and the machine, 2nd edn. MIT Press, CambridgeGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Okinawa Institute of Science and TechnologyOkinawaJapan

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