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Mathematization of nature: how it is done
1Physik Department T35, Technische Universität München, 85747, Garching bei München, Germany. lvh@tum.de.
Biological Cybernetics
|November 27, 2021
Summary
Mathematizing nature requires core concepts and appropriate scales, as demonstrated in physics and biology. Scientific progress depends on rigorous experimental verification of these mathematical descriptions.
Area of Science:
- Explores the quantitative description of natural phenomena across diverse scientific disciplines, including physics, chemistry, and biology (epidemiology, neurobiology).
Background:
- Investigates the process of mathematization, detailing how natural phenomena are translated into mathematical language.
- Highlights physics as a prime example of successful nature mathematization.
Discussion:
- Proposes that mathematizing nature necessitates appropriate core concepts intrinsically linked to the phenomena.
- Introduces the scaling hypothesis: specific mathematical descriptions are valid only within defined scales, with different scales allowing for varied conceptual and mathematical approaches.
Key Insights:
- Mathematical descriptions may be universally valid (physics) or context-specific (biology).
- The rigorous gauging of mathematical theories through experimental verification is crucial for scientific advancement.
- Appropriate core concepts and scales are essential prerequisites for mathematizing nature.
Outlook:
- Emphasizes the interdisciplinary applicability of mathematical modeling in understanding complex natural systems.
- Suggests future research directions in refining scale-dependent mathematical frameworks for biological and physical sciences.
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