Mathematical modelling - hiding or guiding?

Bidragets oversatte titel: Matematiske modeller - vejledende eller vildledende?

Publikation: Bidrag til bog/antologi/rapportBidrag til bog/antologiForskningpeer review

Resumé

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.
OriginalsprogEngelsk
TitelMathematics as a Bridge Between the Disciplines : Proceedings of MACAS-2017 Symposium
RedaktørerClaus Michelsen, Astrid Beckmann, Viktor Freiman, Uffe Thomas Jankvist
Antal sider14
Udgivelses stedOdense
ForlagLaboratorium for Sammenhængende Uddannelse og Læring
Publikationsdato2018
Sider15-28
ISBN (Elektronisk)978-87-92321-27-5
StatusUdgivet - 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). Odense: Laboratorium for Sammenhængende Uddannelse og Læring.
Jensen, Jens Højgaard. / Mathematical modelling - hiding or guiding?. Mathematics as a Bridge Between the Disciplines: Proceedings of MACAS-2017 Symposium. red. / Claus Michelsen ; Astrid Beckmann ; Viktor Freiman ; Uffe Thomas Jankvist. Odense : Laboratorium for Sammenhængende Uddannelse og Læring, 2018. s. 15-28
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title = "Mathematical modelling - hiding or guiding?",
abstract = "The increasing scientific management of technology and society, supportedby increasingly powerful information technologies (IT), has lead, and leads toincreasingly widespread use of mathematical models. This development givesrice to a democratic problem: How can ordinary people judge the conclusionsdelivered by mathematical models? Are the conclusions to be believed, since“mathematics do-not lye”? Or is it better to lean on the saying: “there arelies, damned lies and statistics”?In the paper, I will illustrate a crude distinction between mathematical modelsderived from theories, and ad hoc mathematical models without reference tomore global theories.The distinction cannot be used to evaluate, whether specific models are hidingor guiding. Theory-derived models may be too idealized to be trusted. And adhoc models may be trustworthy due to their richness of input data.The value of the distinction is that it makes it clear that some mathematicalmodels, the theory-derived models, besides of the possibility of evaluatingthem by comparing with empirical data, also can be evaluated by theoreticalconsiderations. Evaluating ad hoc models are, in contrast, restricted to bedone by empirical control only.Thus, the distinction between theory-derived models and ad-hoc models mayhelp ordinary people, not to distinguish between trustworthy and nontrustworthy models but to distinguish between the different qualities of theevaluation processes behind different sorts of models.",
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Jensen, JH 2018, Mathematical modelling - hiding or guiding? i C Michelsen, A Beckmann, V Freiman & UT Jankvist (red), Mathematics as a Bridge Between the Disciplines: Proceedings of MACAS-2017 Symposium. Laboratorium for Sammenhængende Uddannelse og Læring, Odense, s. 15-28.

Mathematical modelling - hiding or guiding? / Jensen, Jens Højgaard.

Mathematics as a Bridge Between the Disciplines: Proceedings of MACAS-2017 Symposium. red. / Claus Michelsen; Astrid Beckmann; Viktor Freiman; Uffe Thomas Jankvist. Odense : Laboratorium for Sammenhængende Uddannelse og Læring, 2018. s. 15-28.

Publikation: Bidrag til bog/antologi/rapportBidrag til bog/antologiForskningpeer review

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AU - Jensen, Jens Højgaard

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Y1 - 2018

N2 - The increasing scientific management of technology and society, supportedby increasingly powerful information technologies (IT), has lead, and leads toincreasingly widespread use of mathematical models. This development givesrice to a democratic problem: How can ordinary people judge the conclusionsdelivered by mathematical models? Are the conclusions to be believed, since“mathematics do-not lye”? Or is it better to lean on the saying: “there arelies, damned lies and statistics”?In the paper, I will illustrate a crude distinction between mathematical modelsderived from theories, and ad hoc mathematical models without reference tomore global theories.The distinction cannot be used to evaluate, whether specific models are hidingor guiding. Theory-derived models may be too idealized to be trusted. And adhoc models may be trustworthy due to their richness of input data.The value of the distinction is that it makes it clear that some mathematicalmodels, the theory-derived models, besides of the possibility of evaluatingthem by comparing with empirical data, also can be evaluated by theoreticalconsiderations. Evaluating ad hoc models are, in contrast, restricted to bedone by empirical control only.Thus, the distinction between theory-derived models and ad-hoc models mayhelp ordinary people, not to distinguish between trustworthy and nontrustworthy models but to distinguish between the different qualities of theevaluation processes behind different sorts of models.

AB - The increasing scientific management of technology and society, supportedby increasingly powerful information technologies (IT), has lead, and leads toincreasingly widespread use of mathematical models. This development givesrice to a democratic problem: How can ordinary people judge the conclusionsdelivered by mathematical models? Are the conclusions to be believed, since“mathematics do-not lye”? Or is it better to lean on the saying: “there arelies, damned lies and statistics”?In the paper, I will illustrate a crude distinction between mathematical modelsderived from theories, and ad hoc mathematical models without reference tomore global theories.The distinction cannot be used to evaluate, whether specific models are hidingor guiding. Theory-derived models may be too idealized to be trusted. And adhoc models may be trustworthy due to their richness of input data.The value of the distinction is that it makes it clear that some mathematicalmodels, the theory-derived models, besides of the possibility of evaluatingthem by comparing with empirical data, also can be evaluated by theoreticalconsiderations. Evaluating ad hoc models are, in contrast, restricted to bedone by empirical control only.Thus, the distinction between theory-derived models and ad-hoc models mayhelp ordinary people, not to distinguish between trustworthy and nontrustworthy models but to distinguish between the different qualities of theevaluation processes behind different sorts of models.

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Jensen JH. Mathematical modelling - hiding or guiding? I Michelsen C, Beckmann A, Freiman V, Jankvist UT, red., Mathematics as a Bridge Between the Disciplines: Proceedings of MACAS-2017 Symposium. Odense: Laboratorium for Sammenhængende Uddannelse og Læring. 2018. s. 15-28