“A model may be pictorial, descriptive, qualitative, or generally approximate in nature, or it may be mathematical and quantitative in nature and reasonably precise.”

— Harold Chestnut

Source: Systems Engineering Tools, (1965), p. 108

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Harold Chestnut 27

American engineer 1917–2001

Harold Chestnut (1917–2001) American engineer

Source: Systems Engineering Tools, (1965), p. 108; As cited in: Alberto Ortiz (1992) Systems engineering concept demonstration, process model http://www.dtic.mil/dtic/tr/fulltext/u2/a265469.pdf. p. 12

“The 'language theory' is inadequate as a description of the nature of mathematics.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially of nature, requires a pure portion, lying at the foundation of the empirical, and based upon à priori knowledge of natural things. …the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.”

Immanuel Kant book Metaphysical Foundations of Natural Science

Preface, Tr. https://books.google.com/books?id=OCJLAAAAMAAJ Ernest Belfort Bax (1883)
Metaphysical Foundations of Natural Science (1786)

“The problem is not the math itself, but the blind acceptance and even idolatry we have applied to the quantitative models. These predictive models leave citizens befuddled and unable to defend or criticize model-based decisions. We argue that we should accept the fact that we live in a qualitative world when it comes to natural processes. We must rely on qualitative models that predict only direction, trends, or magnitudes of natural phenomena, and accept the possibility of being imprecise or wrong to some degree. We should demand that when models are used, the assumptions and model simplifications are clearly stated. A better method in many cases will be adaptive management, where a flexible approach is used, where we admit there are uncertainties down the road and we watch and adapt as nature rolls on.”

Orrin H. Pilkey (1934) American ecologist

Interview with Orrin Pilkey & Linda Jarvis-Pilkey https://web.archive.org/web/20080105132439/http://www.columbia.edu/cu/cup/publicity/pilkeyinterview.html.
Useless Arithmetic: Why Environmental Scientists Can’t Predict the Future (2007)

“As is used in connection with systems engineering, a model is a qualitative or quantitative representation of a process or endeavor that shows the effects of those factors which are significant for the purposes being considered. Modeling is the process of making a model. Although the model may not represent the actual phenomenon in all respects, it does describe the essential inputs, outputs, and internal characteristics, as well as provide an indication of environmental conditions similar to those of actual equipment.”

Harold Chestnut (1917–2001) American engineer

Source: Systems Engineering Tools, (1965), p. 108; As cited in: Alberto Ortiz (1992, p. 13)

“The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

“In the quantitative models that appear in leading economics journals and textbooks, nature is taken to be a fixed, indestructible factor of production. The problem with the assumption is that it is wrong: nature consists of degradable resources.”

Partha Dasgupta (1942) British economist

Partha Dasgupta "Nature's role in sustaining economic development." Philosophical Transactions of the Royal Society B: Biological Sciences 365.1537 (2010): 5-11.

“I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics should be applied to nature, and according to which geometry may also be treated, whenever it leads to general and to fruitful results.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Ausdehnungslehre (1844)

“The final truth about a phenomenon resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge of the phenomenon is complete. We go beyond the mathematical formula at our own risk; we may find a model or a picture which helps us understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault. The making of models or pictures to explain mathematical formulas and the phenomena they describe is not a step towards, but a step away from reality; it is like making a graven image of a spirit.”

James Jeans book The Mysterious Universe

The Mysterious Universe (1930)

“Mathematical physics represents the purest image that the view of nature may generate in the human mind; this image presents all the character of the product of art; it begets some unity, it is true and has the quality of sublimity; this image is to physical nature what music is to the thousand noises of which the air is full…”

Théophile de Donder (1872–1957) Belgian physicist

as quoted by Ilya Prigogine in his Autobiography http://nobelprize.org/nobel_prizes/chemistry/laureates/1977/prigogine-autobio.html given at the occasion of Prigogine's 1977 Nobel Prize in Chemistry.

“A model may be pictorial, descriptive, qualitative, or generally approximate in nature, or it may be mathematical and quantitative in nature and reasonably precise.”

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