Algebraic Aspects of Formal Chemical Kinetics

Part of the Studies in the Foundations, Methodology and Philosophy of Science book series (FOUNDATION, volume 4)


It is striking how slight has been the impact of essentially mathematical ideas upon chemistry. Save in those reaches of the subject that are virtually identical with physics (e.g. quantum mechanics) the torch of foundations research has seldom been lit and the chemist has been far less aware than the physicist of the illumination that might be had from the concepts of rationality and structure that are the “euristic vision of mathematical trance” [1]. Such notions as the necessity and sufficiency of conditions, of similarity classes or of invariants wake but few echoes in the canyons of chemistry and attempts to explore the axiomatic strata that may be present in the chemical landscape have been rare. By comparison with physics, it has received scant attention from the philosophers of science, and, though such attentions are regarded by some as a mixed blessing, this has kept chemistry a little apart from the main intellectual current of natural philosophy. Thus, for example, there is no virtually no tract of it that rejoices in the clarity and coherence of the various physical theories that Bunge has axiomatized and considered in his “ Foundations of Physics” [2].


Molecular Species Versus Versus Versus Short Exact Sequence Singular Perturbation Theory Trivalent Graph 
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  1. 1.
    Bridges, robert: The testament of beauty Book I 1. 368.Google Scholar
  2. 2.
    Springer Tracts in Natural Philosophy. Vol. 10. Berlin-Heidelberg-New York: Springer 1967.Google Scholar
  3. 3.
    Bowen, R.M.: Arch. Rational Mech. Anal. 29, 114 (1968). See also Krambeck 317 (1970). The work of M. Feinberg, soon to be published in the same journal, combines some aspects of Bowen’0.s approach with deeper notions of linear algebra.Google Scholar
  4. Sylvester, J. J.: On an application of the new atomic theory to the graphical representation of the invariants and covariants of binary quantics. Amer. J. Math. 1, 64–125 (1878)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Weyl, H.: Philosophy of mathematics and natural science, 2nd edn. Princeton University Press 1949. Appendix D.Google Scholar
  6. 6.
    Lederberg, J.: Proc. Nat. Acad. Sci. U.S.A. 53, 134 (1965).Google Scholar
  7. Sellers, P.H.: Siam J. Appl. Math. 15, 13 (1967). For an introduction to this paper see an exposition by Sellers in, J. Franklin Inst. 290, 113 (1970), and brief mention on pp. 19 and 20 of the review [14]. A further article by Sellers will appear in Arch. Rational Mech. Anal, in late 1971 or soon after.zbMATHGoogle Scholar
  8. 8.
    Tim. 48c. Jowetts Translation, vũv γaρ oũôδεç noj yeveoiv avrœv /jLSfÂivvyisv àXX œç siôoaiv TIVQ ort noré èartv Km éxaorov avrmv Xéyofjiev àgxaç avrà ridé/Lievoi oroixela rov jiavrôςGoogle Scholar
  9. 9.
    The use has apparently been confined to chemistry, though Tyndall in his treatise on Heat (1880) refers to “the doctrine of the conservation of force, or, as I should express it, Physical Stoichiometry”.Google Scholar
  10. Thus carbon, hydrogen and oxygen suffice for large tracts of organic chemistry, as Bridges recognized when he wrote:“… whether it be starch, oil, sugar or alcohol ‘tis ever our old customers, carbon and hydrogen, pirouetting with oxygen in their morris antics” The Testament of Beauty Book III. 11. 935–7.Google Scholar
  11. 11.
    The appropriateness of singular perturbation theory was first discovered by A. Acrivos, J.R. Bowen and A.K. Openheim [Chem. Engng. Sci. 18, 177 (1963)]. For a discussion of the enzyme reaction see F.G. Heineken, H.M. Tsuchiya and R. Aris, Math. Biosci. 1, 95 (1967). Google Scholar
  12. Prater, C.D.,Wei, J., in: Advances in catalysis, vol. 13. New York: Acad. Press 1962.Google Scholar
  13. 13.
    See for example Aris, R.: Ind. Eng. Chem. Fundamentals 3, 28 (1964) and Wei, J.: Ind. Eng. Chem. Fundamentals 4, 61 (1965).Google Scholar
  14. 14.
    For a more general, but still only partial, review see Aris, R.: Mathematical aspects of chemical reaction. Ind. Eng. Chem. 61,17(1969)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  1. 1.Department of Chemical EngineeringUniversity of MinnesotaMinneapolisUSA

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