Abstract
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].
Keywords
- Molecular Species
- Versus Versus Versus
- Short Exact Sequence
- Singular Perturbation Theory
- Trivalent Graph
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.
“Acknowledgment is made to the donors of the petroleum Research Fund, administered by the American Chemical Society, for partial support of this research.”
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bridges, robert: The testament of beauty Book I 1. 368.
Springer Tracts in Natural Philosophy. Vol. 10. Berlin-Heidelberg-New York: Springer 1967.
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.
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)
Weyl, H.: Philosophy of mathematics and natural science, 2nd edn. Princeton University Press 1949. Appendix D.
Lederberg, J.: Proc. Nat. Acad. Sci. U.S.A. 53, 134 (1965).
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.
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 jiavrôς
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”.
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.
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).
Prater, C.D.,Wei, J., in: Advances in catalysis, vol. 13. New York: Acad. Press 1962.
See for example Aris, R.: Ind. Eng. Chem. Fundamentals 3, 28 (1964) and Wei, J.: Ind. Eng. Chem. Fundamentals 4, 61 (1965).
For a more general, but still only partial, review see Aris, R.: Mathematical aspects of chemical reaction. Ind. Eng. Chem. 61,17(1969)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1971 Springer-Verlag Berlin · Heidelberg
About this chapter
Cite this chapter
Aris, R. (1971). Algebraic Aspects of Formal Chemical Kinetics. In: Bunge, M. (eds) Problems in the Foundations of Physics. Studies in the Foundations, Methodology and Philosophy of Science, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80624-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-80624-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-80626-1
Online ISBN: 978-3-642-80624-7
eBook Packages: Springer Book Archive