The Role of Mathematics in the Existence of Science
The relationship between science and mathematics has long been a subject of philosophical debate. Central to this discussion is the question: can science exist without mathematics? This article delves into the essential role of mathematics in the fundamental principles and practices of science, particularly physics, drawing insights from the natural behaviors of infants and the historical context of human cognition.
Infants' Early Theories of Physics
From birth, infants possess basic theories about the world around them. For instance, babies are notably more perplexed when objects follow paths through space instead of vanishing or appearing out of thin air. This phenomenon is rooted in the natural laws of physics, such as the conservation of mass, a principle first articulated by Aristotle in his work 'Physics'.
These early expectations are innate and develop very early, often before language acquisition. When infants encounter surprising or exceptional cases, they engage in longer and more intense visual behaviors, indicative of cognitive confusion. This suggests that the foundations of scientific thought—understanding the continuity and conservation of objects—emerge from a natural, non-linguistic cognitive process.
The Independence of Physics and Language
It is crucial to recognize that physics and the broader concept of science have existed independently of human language. Physics, as the study of the fundamental laws governing the universe, predates Homo sapiens and earlier human species capable of language. Thus, the principles of physics are universal and do not depend on linguistic constructs for their existence.
While human understanding and communication of these principles are mediated through language, the underlying phenomena remain constant regardless of our ability to articulate or share them. Our models and representations of physical behaviors, including mathematical ones, are indeed linguistic. However, this does not imply that the physical phenomena themselves are intrinsically linguistic or dependent on human cognition.
Mathematics as a Language of Science
Mathematics serves as a powerful tool for describing, teaching, and advancing our understanding of physics. Without mathematics, the ability to share and build on scientific knowledge would be significantly inhibited. However, it is essential to distinguish the representation of physical phenomena from the phenomena themselves. Our models of the physical world, including the study of mathematics, are linguistic constructs that help us communicate and reason about these phenomena.
Language itself is a human trait and a common fallacy to project human characteristics onto the natural world. The physical phenomena that physicists study are independent of any human language constructs and exist regardless of our attempts to describe or understand them. Theories and models in physics, whether expressed in mathematical equations or verbal descriptions, are simply means to better comprehend and predict these natural phenomena.
Conclusion
The existence of science, and physics in particular, is not contingent upon the existence of mathematics or language. While these tools enhance our ability to describe, teach, and share scientific knowledge, the fundamental principles and phenomena themselves persist independently. The relationship between science and mathematics is symbiotic, with each providing a lens through which we can better understand the other.