Skip to main content

Systems and Uncertainty: A Geometrical Approach

  • Chapter
Topics in the General Theory of Structures

Part of the book series: Theory and Decision Library ((TDLD,volume 1))

Abstract

Classical mechanics is founded on the assumption that the quantities it studies have an existence of their own, which we may detect and measure, if we care, to any accuracy permitted by experimental know-how. Quantum mechanics sets theoretical limits to the accuracy we may achieve in the measurement of some quantities; their “existence” is not its object, the formalism deals with “phenomena”, not “noumena”. What about the general systems of Cybernetics (or “General Systems Theory”, or any of the more or less synonymic denominations that abound)? A major advance in scientific thought and philosophy has been the realization that all theories are (more or less successful) “models”: man-made, that is, so that the metaphysical notion of “truth”, attached in turn to Newton’s or Einstein’s descriptions of gravitation, to mention the most classic example, has lost its absolute connotation. The search for better, or just alternative models for gravitation and everything else fills all scientific journals.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.E. Kalman: Proc.Int.Symp. on Dynamical Systems, ed. A.Bednarek: Current Developments in the Interface: Economics, Econometrics, Mathematics”, ed. M. Hazewinkel and A.H.G. Rinnooy Kan ( Dordrecht, D. Reidel, 1982 ).

    Google Scholar 

  2. E.R.Caianiello: Lettere Nuovo Cimento, 25, 225 (1979);27, 89 (1980); 38, 539 (1983); 35, 381 (1982); Nuovo Cimento, 59B, 358(1980); Proc.VV Conf. on Quantum Theory and the Structure of Space and Time,Tutzing (1981); Proc.VI JINR Int. Conf. on Problems of Quantum Theory, Alushta (1980); (with G.Vilasi); Lettere Nuovo Cimento, 30, 469 (1981); (with G.Vilasi and S.De Filippo) ib, 33, 555 (1982);(with G.Marmo and G.Scarpetta), ib, 36, 487 (T383j several other papers in print.

    Google Scholar 

  3. E.T. Jaynes: Phys.Revs., 106, 620 (1952); in Brandeis Theor.Phys. Lecture on Statistical Physics, 3 (New York).

    MathSciNet  Google Scholar 

  4. E.R.Caianiello: Lettere Nuovo Cimento, 38, 539 (1983).

    Article  Google Scholar 

  5. M. Tribus: Rational Descriptions decisions and designs, Pergamon Press, Oxford, (1969).

    Google Scholar 

  6. H. Jeffeey: Theory of Probability, 2nd ed., Clarenton Press, Oxford, (1948).

    Google Scholar 

  7. R.A. Fisher: Phil.Trans.Roy.soc., 22A, 309 (1921); Proc.Cambridge Phil.Soc., 122, 700 (1925).

    Google Scholar 

  8. R.A. Fisher: Proc.Cambridge Phil.Soc., 122, 700 (1925).

    Google Scholar 

  9. S.Amari: Raag.Reps., 106, Feb.1980; Techn.Reps.Fac.Eng.Univ.of Tokyo, METR 81–1, April 1981, ib METR 84–1, Jan.1984;

    Google Scholar 

  10. B.Efron: Ann.Statist., T 1189 (1975); 6, 362 (1978).

    Google Scholar 

  11. A.P. David: Ann.Statist., 3, 1231 (1975)1 5, 1249 (1977).

    Google Scholar 

  12. J.N. Kapur: Journ.Math.Phy.Sci., 17, 103 T1983).

    MathSciNet  MATH  Google Scholar 

  13. N.N. Chentzov: Statistical Decision Rules and Optimal Conclusions (in Russian) Moscow, (1972).

    Google Scholar 

  14. C.R. Rao: Linear statistical Inference and its applications, J.Wiley, New York, (1973) and papers quoted therm.

    Book  MATH  Google Scholar 

  15. R.A.Fisher: cf. Ref.7,b.

    Google Scholar 

  16. E.R. Caianiello, G. Marmo, G. Scarpetta: ‘(Pre)quantum Geometry’, Nuovo Cimento, 38, 539 (1983).

    Article  Google Scholar 

  17. E.R. Caianiello: Lettere Nuovo Cimento, 32, 65 (1981); (with S.De Filippo, G.Marmo, G.Vilasi), ib, 34, 112 (1982); others in print.

    Article  MathSciNet  Google Scholar 

  18. A.D. Sacharov: JETP Letters, 3, 288 (1966).

    Google Scholar 

  19. E.R. Caianiello, G. Land: Lettre Nuovo Cimento, 42, 70 (1985).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 D. Reidel Publishing Company

About this chapter

Cite this chapter

Caianiello, E.R. (1987). Systems and Uncertainty: A Geometrical Approach. In: Caianiello, E.R., Aizerman, M.A. (eds) Topics in the General Theory of Structures. Theory and Decision Library, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3819-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3819-9_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8199-3

  • Online ISBN: 978-94-009-3819-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics