1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

The Study of Man. By Michael Polanyi. Price, $1.75. Pp. 102. University of Chicago Press, 5750 Ellis Ave., Chicago 37, 1959. One subtitle to Polanyi's challenging and fascinating book might be The Evolution and Natural History of Error , for Polanyi is at pains to expunge what he believes to be the false notion contained in the contemporary view of science which treats it as an object and basically impersonal discipline. According to Polanyi not only is this a radical and important error, but it is harmful to the objectives of science itself. Another subtitle could be Farewell to Detachment , for in place of cold objectivity he develops the idea that science is necessarily intensely personal. It is a human endeavor and human point of view which cannot be divorced from nor uprooted out of the human matrix from which it arises and in which it works. For a good while

Personal Knowledge: Towards a Post-Critical Philosophy

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

Foundations Of Statistics

หนงสอ Behavioral Game Theory: Experiments in Strategic Interaction เขยนโดย Colin F. Camerer มวตถประสงคเพอนำเสนอหลกฐานเชงประจกษจากผลการวจยจำนวนมากมายทยนยนอทธพลของปจจยทางจตวทยาทมผลตอการตดสนใจตามทฤษฎเกม หนงสอ เลมนไดนำเสนอแนวคดทฤษฎทเพมความสามารถในการอธบายพฤตกรรมการตดสนใจตามทฤษฎเกม (Game theory) ซง von Neumann; & Morgenstern ไดเสนอไวในป ค.ศ. 1944 โดยชใหเหนวา ปจจยทางจตวทยามอทธพลทำใหการตดสนใจทเกดขนจรงคลาดเคลอนจากการคาดการณของทฤษฎเกม

Behavioral Game Theory: Experiments in Strategic Interaction

In this paper I attempt to show that mathematical economics is unreasonably ineffective. Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalizations imply non-constructive and uncomputable structures. A reasonable and effective mathematization of economics entails Diophantine formalisms. These come with natural undecidabilities and uncomputabilites. In the face of this, I conjecture that an economics for the future will be freer to explore experimental methodologies underpinned by alternative mathematical structures. The whole discussion is framed within the context of the celebrated Wignerian theme: The Unreasonable Effectiveness of Mathematics in the Natural Sciences.

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The Unreasonable Ineffectiveness of Mathematics in Economics.

In this paper, the origins and development of behavioural economics, beginning with the pioneering works of Herbert Simon and Ward Edwards, are traced and (critically) discussed. Two kinds of behavioural economics – classical and modern – are attributed, respectively, to the two pioneers. The mathematical foundations of classical behavioural economics are identified, largely, to be in the theory of computation and computational complexity; the mathematical basis for modern behavioural economics is claimed to be a notion of subjective probability. Individually rational economic theories of behaviour, with attempts to broaden – and deepen – the notion of rationality, challenging its orthodox variants, were decisively influenced by these two mathematical underpinnings.

Behavioural economics: Classical and modern

https://www.math.tecnico.ulisboa.pt/~camado/eim2016/vela_JF.pdf

Uncomputability and undecidability in economic theory

Algorithmic foundations of computable general equilibrium theory

Part I: Foundations 1. The Incomputable, the Non-constructive and the Undecidable in Mathematical Economics 2. Advanced Computational Complexity Theory from an Elementary Standpoint 3. Economic Dynamics and Computation - Recursion Theoretic Foundations for the Icarus Tradition 4: Let's Take the Con out of Mathematical Economics Part II: General Equilibrium Theory 5. Effectivity and Constructivity in Economic Theory 6. Algorithmic Foundations of Computable General Equilibrium Theory 7. Uncomputability and Undecidability in Economic Theory Part III: Methodology 8. The Unreasonable Ineffectivity of Mathematics in Economics 9. A Constructive Interpretation of Sraffa's Mathematical Economics 10. The Computable Alternative in the Mathematization of Economics Part IV: Simon's Behavioural Economics - A Computable Vision 11. Computable Rationality 12. Boundedly Rational Choice and Satisficing Decisions 13. Simon's Epicurean Adventures - A Prolegomena. Appendix 1 to Part IV: Artificing a Rationally Unbounded Life. Appendix 2 to Part IV: The Logic of Discovery, Problem Solving and Retroduction. Appendix 3 to Part IV: Herbert Simon's Letter on Computable Economics Part V: Inductive Reflections 14. De-Mystifying Induction, Falsification and other Popperian Extravaganzas 15. Re-reading Jevons's Principles of Science: Induction Redux 16. Impossibility of Effectively Computable Inductive Policies in a Complex Dynamic Economy. Part VI: Concluding Notes 17. Epilogue - A Research Program for the Algorithmic Social Sciences

/pdf/computable-foundations-for-economics-2k7dul687s.pdf

K. Vela Velupillai

Papers

The Unreasonable Ineffectiveness of Mathematics in Economics.

Behavioural economics: Classical and modern

Uncomputability and undecidability in economic theory

Algorithmic foundations of computable general equilibrium theory

Computable Foundations for Economics