Is Physics Independent of Mathematics?

Understanding the relationship between physics and mathematics is a fundamental question in the sciences. While many debate whether physics relies on mathematics, it is clear that both are deeply intertwined yet distinct. From the earliest stages of human cognition, there are innate expectations about how the physical world behaves, which can be considered basic theories of physics. However, does the study of physics require mathematics, or is it an independent branch of natural philosophy?

The Birth of Physics

The origin of physics predates the advent of Homo Sapiens and even earlier hominids that possessed rudimentary forms of communication. This implies that the principles of physics and the keen observations of natural phenomena existed long before the invention of language. The ideas of Gauss, Newton, and Einstein are legacies of human thought, but the phenomena they described are universal and endure regardless of our understanding.

Early Physics and Human Cognition

Even babies have an intuitive understanding of the physical world. From a very young age, they have consistent expectations, or theories, about how objects should behave. For example, babies are confused when objects abruptly disappear or reappear, reflecting Aristotle’s atcharismos echthnon or ex nihilo nihil fit — "nothing comes from nothing." This expectation is a natural part of human cognition and arises early, suggesting that it is inherent and not learned through language.

When we look at this from a different perspective, physics can be defined as a study involving statements or propositions, in which case human language becomes a critical tool. Without language, our ability to communicate, describe, and build upon our knowledge of physics would be severely limited. However, this does not mean that physics itself is linguistic. The underlying phenomena and laws of physics exist independently of human language and cultural constructs.

Physics and Mathematical Language

Physics models and theories are indeed linguistic constructs, employing mathematical expressions to describe the behavior of physical systems. Mathematical language is a powerful tool for expressing and exploring the principles of physics. However, it is important to understand that the mathematical descriptions are not the phenomena themselves. The behavior of electrons, the trajectory of planets, and the flow of fluids are physical phenomena that exist independently of our mathematical representation of them.

The laws of physics describe how the universe behaves, and these laws are discovered and refined through observation and experimentation. The mathematical language used to express these laws is a product of human thought and a means to communicate and build upon these discoveries. The underlying phenomena—what is happening in the physical world—are grounded in the fundamental laws of nature, which are robust and unchanged by linguistic conventions.

Conclusion

In summary, while the study and communication of physics rely on mathematical language, the underlying principles and phenomena of physics exist independently of language and mathematics. Physics is a branch of natural philosophy that studies the fundamental laws governing the universe, and these laws are universal and enduring. Mathematical language is merely a tool to help us explore, describe, and understand these laws more effectively.