### Abstract

The increasing scientific management of technology and society, supported

by increasingly powerful information technologies (IT), has lead, and leads to

increasingly widespread use of mathematical models. This development gives

rice to a democratic problem: How can ordinary people judge the conclusions

delivered by mathematical models? Are the conclusions to be believed, since

“mathematics do-not lye”? Or is it better to lean on the saying: “there are

lies, damned lies and statistics”?

In the paper, I will illustrate a crude distinction between mathematical models

derived from theories, and ad hoc mathematical models without reference to

more global theories.

The distinction cannot be used to evaluate, whether specific models are hiding

or guiding. Theory-derived models may be too idealized to be trusted. And ad

hoc models may be trustworthy due to their richness of input data.

The value of the distinction is that it makes it clear that some mathematical

models, the theory-derived models, besides of the possibility of evaluating

them by comparing with empirical data, also can be evaluated by theoretical

considerations. Evaluating ad hoc models are, in contrast, restricted to be

done by empirical control only.

Thus, the distinction between theory-derived models and ad-hoc models may

help ordinary people, not to distinguish between trustworthy and nontrustworthy models but to distinguish between the different qualities of the

evaluation processes behind different sorts of models.

by increasingly powerful information technologies (IT), has lead, and leads to

increasingly widespread use of mathematical models. This development gives

rice to a democratic problem: How can ordinary people judge the conclusions

delivered by mathematical models? Are the conclusions to be believed, since

“mathematics do-not lye”? Or is it better to lean on the saying: “there are

lies, damned lies and statistics”?

In the paper, I will illustrate a crude distinction between mathematical models

derived from theories, and ad hoc mathematical models without reference to

more global theories.

The distinction cannot be used to evaluate, whether specific models are hiding

or guiding. Theory-derived models may be too idealized to be trusted. And ad

hoc models may be trustworthy due to their richness of input data.

The value of the distinction is that it makes it clear that some mathematical

models, the theory-derived models, besides of the possibility of evaluating

them by comparing with empirical data, also can be evaluated by theoretical

considerations. Evaluating ad hoc models are, in contrast, restricted to be

done by empirical control only.

Thus, the distinction between theory-derived models and ad-hoc models may

help ordinary people, not to distinguish between trustworthy and nontrustworthy models but to distinguish between the different qualities of the

evaluation processes behind different sorts of models.

Originalsprog | Engelsk |
---|---|

Titel | Mathematics as a Bridge Between the Disciplines : Proceedings of MACAS-2017 Symposium |

Redaktører | Claus Michelsen, Astrid Beckmann, Viktor Freiman, Uffe Thomas Jankvist |

Antal sider | 14 |

Udgivelses sted | Odense |

Forlag | Laboratorium for Sammenhængende Uddannelse og Læring |

Publikationsdato | 2018 |

Sider | 15-28 |

ISBN (Elektronisk) | 978-87-92321-27-5 |

Status | Udgivet - 2018 |

## Citer dette

Jensen, J. H. (2018). Mathematical modelling - hiding or guiding? I C. Michelsen, A. Beckmann, V. Freiman, & U. T. Jankvist (red.),

*Mathematics as a Bridge Between the Disciplines: Proceedings of MACAS-2017 Symposium*(s. 15-28). Laboratorium for Sammenhængende Uddannelse og Læring. https://www.sdu.dk/da/om_sdu/institutter_centre/lsul/skriftserie