Physica A 340 (2004) 656–667 www.elsevier.com/locate/physa The physics of time and dimension in the economics of nancial control Martin Shubik a ; ∗ , Eric Smith b a Cowles Foundation, Yale University, 30 Hillhouse Ave., New Haven, CT 06511, USA b Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA Received 15 November 2003; received in revised form 26 February 2004 Abstract The provision of the goods and services of a modern economy is controlled by a multiplicity of nancial instruments. The basic properties of these instruments are considered here. c  2004 Elsevier B.V. All rights reserved. PACS: 89.65.gH; 89:75: - k Keywords: Financial instruments; Contracts; Transition matrix; Dimensional analysis; Time scale 1. Introduction The physical aspects of any economy are reected in the tangibles of physical and human capital. The employment of these resources is for the most part guided by a complex of money and nancial instruments represented by contracts of varying complexity. In this note our concern is a parsimonious description of the physical economy and the nancial instruments which guide it. In particular, we consider the properties of a minimal collection of basic nancial instruments from which other more complex instruments can be constructed. In economic life many rich institutional forms provide considerable variety in de- livering the basic functions which must be provided to any viable complex economy. In a previous publication (see Ref. [1] also Ref. [2, Chapter 2]) a sketch was given of the structure of the basic nancial instruments of an economy. Here we re-examine and make more precise the sketch suggested there. * Corresponding author. Tel.: +1-203-432-3694; fax: +1-203-432-6167. E-mail address: martin.shubik@yale.edu (M. Shubik). 0378-4371/$-see front matter c  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2004.05.026