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.
| Bidragets oversatte titel | Matematiske modeller - vejledende eller vildledende? |
|---|---|
| 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 |
| Udgivelsessted | Odense |
| Forlag | Laboratorium for Sammenhængende Uddannelse og Læring |
| Publikationsdato | 2018 |
| Sider | 15-28 |
| ISBN (Elektronisk) | 978-87-92321-27-5 |
| Status | Udgivet - 2018 |