1. On the Use of Models in Science

Abstract

This chapter discusses the conceptual foundations and roles of scientific modeling. It categorizes models from living organisms to mathematical equations, analyzing their purposes and limitations as simplified representations that distill complexity. Key principles are explored, establishing that models are strategic idealizations rather than perfect replicas, requiring skill in productive simplification. Models are framed as epistemic tools that generate hypotheses and organize empirical research to iteratively refine theories over time through explanatory or predictive functions. By synthesizing these philosophical underpinnings, the chapter conveys modeling as a balance between art and science that sustains open-ended scientific progress through provisional frameworks and evolving abstraction informed by empirical evidence.

Introduction¶

Science seeks to understand the natural systems that make up our world. Whether it is cells, climate or evolution of life, the phenomena investigated involve countless interacting components operating across multiple scales. To address such complexity, scientists employ models that are simplified representations aimed at distilling the key features of the system under study, while ignoring less important details. Models take diverse forms, ranging from living organisms and physical constructions to mathematical equations and conceptual diagrams. Despite their different representations, all models seek to condense complexity into forms comprehensible to the human mind.

The development of models is fundamental in several scientific disciplines. Among other applications, models facilitate hypothesis testing and theoretical development when direct experimentation is difficult. It could even be argued that scientific theories themselves are models that provide simplified frameworks for explaining and predicting natural phenomena.

This chapter explores the conceptual foundations and functions of modeling in science. It details the various types of model and investigates their philosophical foundations. The ideas presented synthesize information extracted from these sources: Rosenblueth & Wiener (1945), Borges (1982), Box (1976).

Categories of Scientific Models¶

Scientific models simplify the complexity of natural systems through various forms of representation designed to serve specific purposes. In general, models may be classified into four categories ordered from less to more abstract:

Living Organisms as Models¶

Some living organisms such as rodents, zebrafish, fruit flies, bacteria and other species are used as models to simulate key aspects of human biology, or biology of other species of interest, and the underlying mechanisms of disease. Since they involve living organisms, these models capture the inherent systemic complexity of life that cannot be replicated through other types of models.

Living models offer benefits such as allowing the study, under controlled conditions and in a longitudinal way, of dynamic and complex biological processes such as development, physiology and the progression of diseases. This allows understanding such processes in the functional multisystemic context of the living organism. Likewise, animal testing enables pre-clinical evaluation of drug efficacy, safety and optimal dosing regimens before clinical trials with human subjects. This ensures, as far as possible, the protection of health and well-being of participants in human research.

However, they also have certain limitations. The inherent complexity of living organisms makes it difficult to isolate and study individual molecular or physiological variables, making it difficult to establish direct cause-effect links. In addition, biological differences between species require extrapolating animal data to humans, as not all disease mechanisms can be directly comparable due to evolutionary divergence.

In summary, while offering a more holistic approximation of human biology, or biology of species of commercial interest, than other models, they must be evaluated according to intrinsic limitations and ethical factors, to ensure they continue to significantly contribute to advances in biomedicine.

Physical Models¶

Physical models are concrete material representations of biological structural elements. Some historically relevant examples are physical prototypes of the DNA double helix and various protein complexes. These models describe key attributes such as molecular geometry and conformational changes in a tangible and visualizable way.

Physical models offer certain advantages for research and education. Their practical nature facilitates visualization and conceptualization of abstract biomolecular organizations. This interactive characteristic inspires new hypotheses and experiments as researchers manipulate the replicas. They also effectively convey structural concepts to students and broad audiences.

However, they also have inherent limitations due to their nature. The replicas necessarily simplify and omit small-scale features. Consequently, they provide a simplified representation that can obscure subtle but biologically relevant interactions.

Conceptual Models¶

Conceptual models use diagrams, analogies and other visual and verbal frameworks to represent systems qualitatively. They include descriptions of biological structures such as the circulatory system or the atomic system. Conceptualizations also encompass descriptive illustrations of dynamic processes and networks.

The main advantages of conceptual models lie in their ability to distill abstract relationships and emergent properties into mentally comprehensible forms. Visual diagrams and verbal abbreviations communicate general functional principles accessibly. This ability makes them highly effective tools for interdisciplinary exchange and building conceptual foundations.

However, qualitative abstraction also involves limitations. These models omit specific mechanisms and numerical data, which can limit their applicability to answering quantitative questions. Their generality facilitates communication but risks oversimplification or spreading unelaborated concepts. Overall, their explanatory power depends on the nature of the research problem and the availability of complementary approaches.

Mathematical Models¶

Mathematical models express relationships through symbolic equations and formulas that quantify natural phenomena. Some examples are equations describing population growth, disease spread and kinetics of biochemical reactions.

A key advantage is their ability to rigorously characterize systems through numerical parameters and functions. When parameterized with experimental data, they enable predictive and testable forecasting. Their quantitative nature also facilitates hypothesis testing through numerical simulations. They also allow integrating diverse data sets and implementing hierarchical modeling across multiple scales.

However, quantitative precision depends on establishing appropriate functional forms and empirically estimating parameters. Gaps or uncertainties in available data can reduce predictive power or require simplifying assumptions. The quantitative approach also requires scoping the focus to avoid analytically or numerically intractable complexities. As a result, they work best when focused on well-defined subsystems.

When constructed and applied correctly, mathematical models constitute a powerful tool. But their ability to represent reality depends on empirical knowledge of the system under study and incorporating idealizations that make them analytically or numerically tractable.

Together, the model categories outlined here, from animal models to mathematical formalisms, capture the diverse yet complementary ways in which scientific abstraction seeks to understand intricate natural phenomena. Each paradigm offers benefits while possessing inherent limitations that delimit its applicability.

Philosophy of Scientific Modeling¶

While models take diverse forms, they share a common philosophical perspective regarding the simplification of reality. The following analyzes some key principles underpinning scientific modeling.

Models as Idealizations¶

Developing models entails an abstraction process aimed at distilling the essence of complexity through simplification and interpretation. As Rosenblueth and Wiener expressed, perfectly replicating a system would require the model to be identical to the object, losing its usefulness.

This is comically illustrated in Borges’ story of a fictional empire in which the science of cartography becomes so exact that it ultimately elaborates a single map at the empire’s own scale. These ideas emphasize that models avoid being perfect replicas to become manageable representations of the systems under study.

The goal is thus abstraction through which the essential is condensed in simplified constructions cognizable. Modeling seeks to reveal the essence beneath through idealization, not mere imitation of details. This could be summarized in George Box’s following statement: “Although all models are wrong, some prove useful.” The standard is not strict precision but the ability to shed light on scientific questions through strategic abstraction and simplification.

The Art of Productive Simplification¶

Developing a useful model requires discerning which details can be omitted and which must be included to answer specific scientific questions. Too much abstraction can generate non-informative models, while insufficient abstraction hinders analysis.

There is an “art” to selective idealization. According to Rob Phillips, incorporating simplifications that preserve core behaviors and mechanisms, reducing ancillary details, can inspire new perspectives. Phillips distinguishes between errors of idealization, by omitting non-essential factors, and objective errors, by mis-characterizing the phenomenon. The former may be acceptable if they do not affect the model’s functions; the latter are less permissible.

The test of simplifications lies in whether they support models’ understanding and predictive capacity more than strict similarity to reality. There is no precise methodology to determine which simplifications are acceptable and which are not, as this judgment depends on the modeler’s experience and intuition.

Models as Epistemic Tools¶

Due to their simplified and abstract nature, scientific models serve as epistemic tools rather than definitive representations of reality. It is better to understand them as operational frameworks that drive scientific inquiry.

By condensing complexity, models configure empirical research and point to novel scientific lines of work. Their value lies more in stimulating novel scientific questions than in definitively closing projects. In this sense, they catalyze iterative refinement of knowledge over time.

In the context of mathematical models, these can be explanatory or predictive. The former formalize causal relationships, representing and testing dynamics to deepen understanding through predictions that can be experimentally tested. The latter focus on providing accurate forecasts by integrating patterns and trends.

Both types of models advance knowledge in different yet complementary ways. Explanatory models provide mechanistic perspectives. When their predictions are substantiated with experimental outcomes, they help consolidate theoretical frameworks. Predictive models provide reliable forecasts. Together, these approaches advance understanding through hypotheses, theoretical synthesis, questions and evidence-based decisions.

Discussion¶

This chapter has examined the foundations and roles of scientific modeling. In summary, developing models requires expertise in creating productive simplifications that preserve explanatory or predictive functionality. This implies a balance between art and science: data substantiate but abstraction remains an interpretive process.

Looking ahead, modeling will become even more important as technologies reveal greater details of systems. Progress will depend on interaction between simplification, experimentation and iterative theoretical refinement.

Models ensure that scientific inquiry remains an empirical, mentally open process. By establishing provisional understandings, they invite dialogue and extension of theories in the face of emergent realities. This sustains the central role of modeling in science.

While natural mysteries surpass human comprehension, modeling guarantees perpetual advancement through abstraction levels. Gradually revealing the intricate designs of nature, it propels both discovery and a deeper understanding of natural complexity across diverse spatiotemporal scales.