Abstract
In his famous article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” Eugen Wigner argues for a unique tie between mathematics and physics, invoking even religious language: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve” (Wigner 1960: 1). The possible existence of such a unique match between mathematics and physics has been extensively discussed by philosophers and historians of mathematics (Bangu 2012; Colyvan 2001; Humphreys 2004; Pincock 2012; Putman 1975; Steiner 1998). Whatever the merits of this claim are, a further question can be posed with regard to mathematization in science more generally: What happens when we leave the area of theories and laws of physics and move over to the realm of mathematical modeling in interdisciplinary contexts? Namely, in modeling the phenomena specific to biology or economics, for instance, scientists often use methods that have their origin in physics. How is this kind of mathematical modeling justified?
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Notes
- 1.
- 2.
This notion of a “reasonably self-contained system” bears an interesting link to the theme of fiction discussed below in Sect. 5.
- 3.
- 4.
Other scientists such as Brian Goodwin take the binding of the RNAp into account. This makes the differential equations more difficult by adding a further variable.
- 5.
On the notion of an epistemic tool, see Knuuttila (2011).
- 6.
For example, the properties and dynamic features of network motifs describing recurrent structures in genetic networks (e.g. feedforward and feedback loops) can be analyzed by making use of the Michaelis-Menten equations (Berg et al. 2002).
- 7.
Personal communication by Michael Elowitz.
- 8.
Even if all the active sites of the proteins are occupied by repressors one observes some production of proteins, which is expressed by α 0.. This is what is meant by leakiness.
- 9.
This draws synthetic modeling close to simulation modeling, which brings to mathematical modeling exploratory and experimental features (e.g., Lenhard 2007).
References
Alon, U. (2006). An introduction to systems biology. London: Chapman & Hall/CRC Mathematical and Computational Biology.
Bangu, S. (2012). The applicability of mathematics in science: Indispensability and ontology. Basingstoke: Palgrave Macmillan.
Berg, J. M., Tymoczko, J. L., & Stryer, L. (2002). Biochemistry. New York: W. H. Freeman.
Bujara, M., Schümperli, M., Pellaux, R., Heinemann, M., & Panke, S. (2011). Optimization of a blueprint for in vitro glycolysis by metabolic real-time analysis. Nature Chemical Biology, 7, 271–277.
Çağatay, T., Turcotte, M., Elowitz, M. B., Garcia-Ojalvo, J., & Suel, G. M. (2009). Architecture-dependent noise discriminates functionally analogous differentiation circuits. Cell, 139(3), 1–11.
Chalfie, M., Yuan, T., Euskirchen, G., Ward, W. W., & Prasher, D. C. (1994). Green fluorescent protein as a marker for gene expression. Science, 263(5148), 802–805.
Church, G. M. (2005). From systems biology to synthetic biology. Molecular Systems Biology, 1.
Colyvan, M. (2001). The indispensability of mathematics. New York: Oxford University Press.
Elowitz, M. B., & Leibler, S. (2000). A synthetic oscillatory network of transcriptional regulators. Nature, 403(6767), 335–338.
Elowitz, M. B., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–890.
Elowitz, M. B., Surette, M. G., Wolf, P.-E., Stock, J., & Leibler, S. (1997). Photoactivation turns green fluorescent protein red. Current Biology, 7(10), 809–812.
Elowitz, M. B., Levine, A. J., Siggia, E. D., & Swain, P. S. (2000). Stochastic gene expression in a single cell. Science, 297(5584), 1183–1186.
Godfrey-Smith, P. (2009). Models and fictions in science. Philosophical Studies, 143(1), 101–116.
Goodwin, B. (1963). Temporal organization in cells. London, New York: Academic Press.
Hesse, M. B. (1966). Models and analogies in science. Notre Dame: Notre Dame University Press.
Humphreys, P. (2004). Extending ourselves: Computational science, empiricism, and scientific method. Oxford: Oxford University Press.
Jacob, F., & Monod, J. (1961). Genetic regulatory mechanisms in the synthesis of proteins. Journal of Molecular Biology, 3(3), 318–356.
Khalil, A. S., & Collins, J. J. (2010). Synthetic biology: application come to age. Nature Reviews Genetics, 11(5), 367–379.
Knuuttila, T. (2009). Representation, idealization, and fiction in economics: From the assumptions issue to the epistemology of modelling. In M. Suárez (Ed.), Fictions in science: Philosophical essays on modeling and idealization (pp. 205–231). New York/London: Routledge.
Knuuttila, T. (2011). Modeling and representing: An artefactual approach. Studies in History and Philosophy of Science, 42(2), 262–271.
Knuuttila, T., & Loettgers, A. (2011). The productive tension: Mechanisms vs. templates in modeling the phenomena. In P. Humphreys & C. Imbert (Eds.), Representations, models, and simulations (pp. 3–24). New York: Routledge.
Knuuttila, T., & Loettgers, A. (2013). Basic science through engineering: Synthetic modeling and the idea of biology-inspired engineering. Studies in History and Philosophy of Biological and Biomedical Sciences, 44(2), 158–169.
Knuuttila, T., & Loettgers, A. (2014). Varieties of noise: Analogical reasoning in synthetic biology. Studies in History and Philosophy of Science Part A, 48, 76–88.
Knuuttila, T., & Loettgers, A. (2016). Modelling as indirect representation? The Lotka-Volterra model revisited. British Journal for the Philosophy of Science. doi:10.1093/bjps/axv055.
Lenhard, J. (2007). Computer simulation: The cooperation between experimenting and modeling. Philosophy of Science, 74(2), 176–194.
Loettgers, A. (2009). Synthetic biology and the emergence of a dual meaning of noise. Biological Theory, 4(4), 340–349.
Marguéz-Lago, T., & Stelling, J. (2010). Counter-intuitive stochastic behavior of simple gene circuits with negative feedback. Biophysical Journal, 98(9), 1742–1750.
Nandagopal, N., & Elowitz, M. B. (2011). Synthetic biology: Integrated gene circuits. Science, 333(6047), 1244.
Pincock, C. (2012). Mathematics and scientific representation. Oxford and New York: Oxford University Press.
Pittendrigh, C. S. (1961). On temporal organization in living systems. The Harvey Lectures, 59, 63–125.
Putman, H. (1975). What is mathematical truth? Historia Mathematica, 2(4), 529–533.
Rouse, J. (2009). Laboratory fictions. In M. Suárez (Ed.), Fictions in science: Philosophical essays on modeling and idealization (pp. 37–55). New York/London: Routledge.
Sprinzak, D., & Elowitz, M. B. (2005). Reconstruction of genetic circuits. Nature, 438(7067), 443–448.
Steiner, M. (1998). The applicability of mathematics as a philosophical problem. Cambridge, MA: Harvard University Press.
Suárez, M. (2009). Fictions in science: Philosophical essays on modeling and idealization. New York: Routledge.
Süel, G. M., Kulkarni, R. P., Dworkin, J., Garcia-Ojalvo, J., & Elowitz, M. B. (2007). Tunability and noise dependence in differentiation dynamics. Science, 315(5819), 1716–1719.
Swain, P. S., Elowitz, M., & Siggia, E. D. (2002). Intrinsic and extrinsic contributions to stochasticity in gene expression. Proceedings of the National Academy Sciences, 99(20), 12795–12800.
Thomas, R., & D’Ari, R. (1990). Biological feedback. Boca Raton: CRC Press.
Weisberg, M. (2007). Three kinds of idealization. The Journal of Philosophy, 104(12), 639–659.
Wigner, E. P. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Communication on Pure and Applied Mathematics, 13(1), 1–14.
Winfree, A. (1967). Biological rhythms and the behavior of populations of coupled oscillators. Journal of Theoretical Biology, 16(1), 15–42.
Winfree, A. (2001). The geometry of biological time. Heidelberg/New York: Springer.
Zhang, F., Rodriquez, S., & Keasling, J. D. (2011). Metabolic engineering of microbial pathways for advanced biofuels production. Current Opinion in Biotechnology, 22(6), 775–783.
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Knuuttila, T., Loettgers, A. (2017). Mathematization in Synthetic Biology: Analogies, Templates, and Fictions. In: Lenhard, J., Carrier, M. (eds) Mathematics as a Tool. Boston Studies in the Philosophy and History of Science, vol 327. Springer, Cham. https://doi.org/10.1007/978-3-319-54469-4_3
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